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2018
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Lothar Heinrich
Asymptotic goodness-of-fit tests for point processes based on scaled empirical K-functions
Statistics 52, 829-851 (2018)
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2017
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Lothar Heinrich
Asymptotic Goodness-of-Fit Tests for Point Processes Based on Scaled Empirical K-Functions
preprint, (2017)
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Christian Bräu and Lothar Heinrich
Mixing properties of stationary Poisson cylinder models
Stochastics 89, 753-765 (2017)
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Lothar Heinrich, Friedrich Pukelsheim and Vitali Wachtel
The variance of the discrepancy distribution of rounding procedures, and sums of uniform random variables
Metrika 80, 363-375 (2017)
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2016
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Lothar Heinrich
Gaussian and Non-Gaussian Stable Limit Laws in Wicksell's Corpuscle Problem
preprint, (2016)
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Christian Bräu and Lothar Heinrich
Mixing Properties of Stationary Poisson Cylinder Models
preprint, (2016)
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Christian Bräu and Lothar Heinrich
Multivariate Poisson distributions associated with Boolean models
Metrika 79, 749-761 (2016)
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Lothar Heinrich
On the strong Brillinger-mixing property of α-determinantal point processes and some applications
Applications of Mathematics 61, 443-461 (2016)
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Lothar Heinrich and Lutz Muche
Some remarks on second-order characteristics of planar Poisson-Voronoi tessellations
Applied Mathematical Sciences 10, 1307-1320 (2016)
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Lothar Heinrich, Friedrich Pukelsheim and Vitali Wachtel
The Variance of the Discrepancy Distribution of Rounding Procedures, and Sums of Uniform Random Variables
preprint, (2016)
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2015
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Lothar Heinrich
Gaussian limits of empirical multiparameter K-functions of homogeneous Poisson processes and tests for complete spatial randomness
Lithuanian Mathematical Journal 55, 72-90 (2015)
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Christian Bräu and Lothar Heinrich
Multivariate Poisson Distributions Associated with Boolean Models
preprint, (2015)
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Lothar Heinrich
On the Strong Brillinger-Mixing Property of Alpha-Determinantal Point Processes and Some Applications
preprint, (2015)
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Lothar Heinrich
Some Inequalities for Chord Power Integrals of Parallelotopes
preprint, (2015)
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2014
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Lothar Heinrich and Mirjam Appelt
A stable limit law for recurrence times of the simple random walk on the two-dimensional integer lattice
Lithuanian Mathematical Journal 54, 308-322 (2014)
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Lothar Heinrich, Sebastian Lück and Volker Schmidt
Asymptotic goodness-of-fit tests for the Palm mark distribution of stationary point processes with correlated marks
Bernoulli 20, 1673-1697 (2014)
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Lothar Heinrich and Stella Klein
Central limit theorems for empirical product densities of stationary point processes
Statistical Inference for Stochastic Processes 17, 121-138 (2014)
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Lothar Heinrich
Gaussian Limits of Empirical Multiparameter K-Functions of Homogeneous Poisson Processes and Tests for Complete Spatial Randomness
preprint, (2014)
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Lothar Heinrich
Lower and Upper Bounds for Chord Power Integrals of Ellipsoids
preprint, (2014)
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Lothar Heinrich
Lower and upper bounds for chord power integrals of ellipsoids
Applied Mathematical Sciences 8, 8257-8269 (2014)
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2013
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Lothar Heinrich and Mirjam Appelt
A Stable Limit Law for Recurrence Times of the Simple Random Walk on the Lattice Z2
preprint, (2013)
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Lothar Heinrich and Zbynek Pawlas
Absolute Regularity and Brillinger Mixing of Stationary Point Processes
preprint, (2013)
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Lothar Heinrich and Zbyněk Pawlas¹
Absolute regularity and Brillinger-mixing of stationary point processes
Lithuanian Mathematical Journal 53, 293-310 (2013)
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Lothar Heinrich and Malte Spiess
Central Limit Theorems for Volume and Surface Content of Stationary Poisson Cylinder Processes in Expanding Domains
Advances in Applied Probability 45, 312-331 (2013)
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2012
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Lothar Heinrich
Asymptotic Methods in Statistics of Random Point Processes
Stochastic Geometry, Spatial Statistics and Random Fields 2068, 115-150 (2012)
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Lecture Notes in Mathematics; 2068
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Lothar Heinrich and Malte Spiess
Central Limit Theorem for the Volume of stationary Poisson Cylinder Processes in Expanding Domains
preprint, (2012)
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Lothar Heinrich, Stella Klein and Martin Moser
Empirical Mark Covariance and Product Density Function of Stationary Marked Point Processes—A Survey on Asymptotic Results
Methodology and Computing in Applied Probability 16, 283-293 (2012)
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Lothar Heinrich, Sebastian Lück and Volker Schmidt
Non-parametric asymptotic statistics for the Palm mark distribution of β-mixing marked point processes
preprint, (2012)
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Lothar Heinrich
Some new results on second-order chord power integrals of convex quadrangles
Supplemento ai Rendiconti del Circolo Matematico di Palermo: Serie II 84, 195-205 (2012)
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Proceedings: VIIIth international conference in "stochastic geometry, convex bodies, empirical measures & applications to mechanics and engineering train-transport”; Taormina - Italy, 28-30 September, 2011
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2011
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Lothar Heinrich, Sebastian Lück and Volker Schmidt
Asymptotic Goodness-of-fit Tests for the Palm Mark Distribution of Stationary Point Processes with Correlated Marks
preprint, (2011)
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Lothar Heinrich and Stella Klein
Central Limit Theorems for Empirical Product Densities of Stationary Point Processes
preprint, (2011)
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Lothar Heinrich and Stella Klein
Central limit theorem for the integrated squared error of the empirical second-order product density and goodness-of-fit tests for stationary point processes
Statistics & Risk Modeling 28, 359-387 (2011)
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Lothar Heinrich
Some New Results on Second-Order Chord Power Integrals of Convex Quadrangles
preprint, (2012)
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2010
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Stella Veronica David and Lothar Heinrich
Central Limit Theorem for the Integrated Squared Error of the Empirical Second-Order Product Density and Goodness-of-fit Tests for Stationary Point Processes
preprint, (2010)
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Lothar Heinrich and Michael Werner
Strongly consistent estimation in Wicksell's corpuscle problem in case of occluded spheres
Advances and Applications in Statistical Sciences 4, 89-164 (2010)
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2009
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Lothar Heinrich and Malte Spiess
Berry-Esseen Bounds and Cramer-Type Large Deviations for the Volume Distribution of Poisson Cylinder Processes
preprint, (2009)
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Lothar Heinrich and Malte Spiess
Berry–Esseen bounds and Cramér-type large deviations for the volume distribution of Poisson cylinder processes
Lithuanian Mathematical Journal 49, 381-398 (2009)
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Lothar Heinrich
Central limit theorems for motion-invariant Poisson hyperplanes in expanding convex bodies
Supplemento ai Rendiconti del Circolo Matematico di Palermo: Serie II 81, 187-212 (2009)
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Proceedings of the VIIth International Conference in “Stochastic Geometry, Convex Bodies, Empirical Measures & Applications to Mechanics and Engineering Train-Transport”; Messina, April 22-24, 2009
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Lothar Heinrich
Mixing Properties and Central Limit Theorem for a Class of Non-Identical Piecewise Monotonic C2 - Transformations
Mathematische Nachrichten 181, 185-214 (2009)
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Lothar Heinrich
On Lower Bounds of Second-Order Chord Power Integrals of Convex Discs
preprint, (2009)
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Lothar Heinrich
On lower bounds of second-order chord power integrals of convex discs
Supplemento ai Rendiconti del Circolo Matematico di Palermo: Serie II 81, 213-222 (2009)
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Proceedings of the VIIth International Conference in “Stochastic Geometry, Convex Bodies, Empirical Measures & Applications to Mechanics and Engineering Train-Transport”; Messina, April 22-24, 2009
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2008
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Lothar Heinrich and Michaela Prokešová
On Estimating the Asymptotic Variance of Stationary Point Processes
Methodology and Computing in Applied Probability 12, 451-471 (2008)
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Lothar Heinrich
On the Miquel point of simplices
Elemente der Mathematik , 126-136 (2008)
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Lothar Heinrich and Lutz Muche
Second-order properties of the point process of nodes in a stationary Voronoi tessellation
Mathematische Nachrichten 281, 350-375 (2008)
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Lothar Heinrich and Zbyněk Pawlas
Weak and strong convergence of empirical distribution functions from germ-grain processes
Statistics 42, 49-65 (2008)
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2007
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Lothar Heinrich
An Almost-Markov-Type Mixing Condition and Large Deviations for Boolean Models on the Line
Acta Applicandae Mathematicae 96, 247-262 (2007)
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Lothar Heinrich
Central Limit Theorems for Motion-Invariant Poisson Hyperplanes in Expanding Convex Bodies
preprint, (2007)
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Lothar Heinrich
Comment in: Discussion of 'Modern Statistics for Spatial Point Processes'
Scandinavian Journal of Statistics 34, 695-696 (2007)
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Lothar Heinrich
Limit distributions of some stereological estimators in Wicksell's corpuscle problem
Image Analysis & Stereology 26, 63-71 (2007)
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Lothar Heinrich, Hendrik Schmidt and Volker Schmidt
Limit theorems for functionals on the facets of stationary random tessellations
Bernoulli 13, 868-891 (2007)
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2006
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Lothar Heinrich, Hendrik Schmidt and Volker Schmidt
Central limit theorems for Poisson hyperplane tessellations
The Annals of Applied Probability 16, 919-950 (2006)
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Lothar Heinrich and Udo Schwingenschlögl
Goodness-of-fit Criteria for the Adams and Jefferson Rounding Methods and their Limiting Laws
Metrika 64, 191-207 (2006)
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Zbyněk Pawlas and Lothar Heinrich
Nonparametric Testing of Distribution Functions in Germ-grain Models
in: Case studies in spatial point process modeling, ed. by Adrian Baddeley, Pablo Gregori, Jorge Mateu, Radu Stoica and Dietrich Stoyan, (Lecture Notes in Statistics book series (LNS), Vol. 185) 125-133 (Springer: New York, NY, 2006)
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Lothar Heinrich and Ilya S. Molchanov
Some Limit Theorems for Extremal and Union Shot-Noise Processes
Mathematische Nachrichten 168, 139-159 (2006)
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2005
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Lothar Heinrich
Large deviations of the empirical volume fraction for stationary Poisson grain models
The Annals of Applied Probability 15, 392-420 (2005)
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Lothar Heinrich, Hendrik Schmidt and Volker Schmidt
Limit theorems for stationary tessellations with random inner cell structures
Advances in Applied Probability 37, 25-47 (2005)
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Lothar Heinrich, Friedrich Pukelsheim and Udo Schwingenschlögl
On stationary multiplier methods for the rounding of probabilities and the limiting law of the Sainte-Laguë divergence
Statistics & Decisions 23, 117-129 (2005)
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2004
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Stephan Böhm, Volker Schmidt and Lothar Heinrich
Asymptotic properties of estimators for the volume fractions of jointly stationary random sets
Statistica Neerlandica 58, 388-406 (2004)
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Stephan Böhm, Lothar Heinrich and Volker Schmidt
Kernel Estimation of the Spectral Density of Stationary Random Closed Sets
Australian & New Zealand Journal of Statistics 46, 41-51 (2004)
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Lothar Heinrich, Friedrich Pukelsheim and Udo Schwingenschlögl
Sainte-Laguë’s chi-square divergence for the rounding of probabilities and its convergence to a stable law
Statistics & Decisions 22, 43-60 (2004)
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2001
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Lothar Heinrich
On the asymptotic behaviour of the integral int 0infty eitx(x-alpha-([xalpha]+1)-1 )dx as t->0 and rates of convergence to alpha-stable limit laws
Zeitschrift für Analysis und ihre Anwendungen 20, 379-394 (2001)
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2000
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Lothar Heinrich and Michael Werner
Kernel estimation of the diameter distribution in boolean models with spherical grains
Journal of Nonparametric Statistics 12, 147-176 (2000)
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1999
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Lothar Heinrich and Ilya S. Molchanov
Central limit theorem for a class of random measures associated with germ-grain models
Advances in Applied Probability 31, 283-314 (1999)
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1998
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Lothar Heinrich and Michael Werner
A Contribution to the Nonparametric Statistics of Particle Systems
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik 78, 941-942 (1998)
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Lothar Heinrich
Contact and chord length distribution of a stationary Voronoi tessellation
Advances in Applied Probability 30, 603-618 (1998)
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Lothar Heinrich, R. Körner, N. Mehlhorn and Lutz Muche
Numerical and Analytical Computation of Some Second-Order Characteristics of Spatial Poisson-Voronoi Tessellations
Statistics 31, 235-259 (1998)
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Lothar Heinrich
On asymptotic estimation in Wicksells corpuscle problem
in: Prague stochastics '98: proceedings of the joint session of 6th Prague symposium on asymptotic statistics & 13th Prague conference on information theory, statistical decision functions and random processes, held from August 23-28, 1998, ed. by Marie Hušková, 227-231 (Union of Czech Mathematicians and Physicists: Prague, 1998)
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1997
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Lothar Heinrich
Absolute regularity of stochastic processes and fields
in: Encyclopaedia of Mathematics. [11]. Supplement Volume I, ed. by Michiel Hazewinkel, 8-9 (Springer Netherlands: Dordrecht, 1997)
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Lothar Heinrich
Poisson approximation for the number of large digits of inhomogeneousf-expansions
Monatshefte für Mathematik 124, 237-253 (1997)
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Lothar Heinrich and Eckhard Liebscher
Strong convergence of kernel estimators for product densities of absolutely regular point processes
Journal of Nonparametric Statistics 8, 65-96 (1997)
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1995
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Lothar Heinrich and Eik Schüle
Generation of the typical cell of a non-poissonian Johnson-Mehl tessellation
Communications in Statistics - Stochastic Models 11, 541-560 (1995)
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F. Götze, Lothar Heinrich and C. Hipp
m-dependent random fields with analytic cumulant-generating function
Scandinavian Journal of Statistics 22, 183-195 (1995)
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1994
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Lothar Heinrich
Normal approximation for some mean-value estimates of absolutely regular tessellations
Mathematical methods of statistics 3, 1-24 (1994)
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Lothar Heinrich and Lutz Muche
On the pair correlation function of the point process of nodes in a Voronoi tessellation
preprint, (Fakultät für Mathematik und Informatik, TU Bergakademie Freiberg: Freiberg, 1994)
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1993
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Lothar Heinrich
Asymptotic properties of minimum contrast estimators for parameters of boolean models
Metrika 40, 67-94 (1993)
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Lothar Heinrich and W. Wolf
On the Convergence of U-Statistics with Stable Limit Distribution
Journal of Multivariate Analysis 44, 266-278 (1993)
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Lothar Heinrich
Tail triviality of point processes and Poisson convergence for some classes of particle motions
preprint, (Fachbereich Mathematik, TU Bergakademie Freiberg: Freiberg, 1993)
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1992
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Lothar Heinrich
Bounds for the absolute regularity coefficient of a stationary renewal process
Yokohama Mathematical Journal 40, 25-33 (1992)
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Lothar Heinrich
Minimum contrast estimates for parameters of spatial ergodic point processes
in: Information theory, statistical decision functions, random processes: transactions of the 11th Prague conference held from August 27 to 31, 1990, ed. by Stanislav Kubík and J. A. Vísek, 479-492 (Kluwer: Dordrecht [u.a.], 1992)
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Lothar Heinrich
Mixing properties of Gibbsian point processes and asymptotic normality of Takacs-Fiksel estimates
preprint, (SFB 343, Universität Bielefeld: Bielefeld, 1992)
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Lothar Heinrich
On existence and mixing properties of germ-grain models
Statistics 23, 271-286 (1992)
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1991
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Lothar Heinrich
Goodness-of-fit tests for the second moment funciton of a stationary multidimensional poisson process
Statistics 22, 245-268 (1991)
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U. Lorz and Lothar Heinrich
Normal and poisson approximation of infinitely divisible distribution functions
Statistics 22, 627-649 (1991)
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1990
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Lothar Heinrich
Asymptotic Expansions in the Central Limit Theorem for a Special Class ofm-Dependent Random Fields II – Lattice Case
Mathematische Nachrichten 145, 309-327 (1990)
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Lothar Heinrich
Non-Uniform Bounds for the Error in the Central Limit Theorem for Random Fields Generated by Functions of Independent Random Variables
Mathematische Nachrichten 145, 345-364 (1990)
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Lothar Heinrich
Some Bounds of Cumulants of m-Dependent Random Fields
Mathematische Nachrichten 149, 303-317 (1990)
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Lothar Heinrich and A. Schwandtke
Some Remarks on Second-Order-Analysis of Planar Fibre Processes by Line Intersections
Mathematische Nachrichten 146, 247-257 (1990)
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1989
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Lothar Heinrich and W. Wolf
Uniform and non-uniform approximations of U-statistics by stable distributions
in: Proceedings of the Fourth Prague Symposium on Asymptotic Statistics: 29 August - 2 September 1988, ed. by Petr Mandl, 249-257 (Charles Univ.: Prague, 1989)
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1988
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Lothar Heinrich
Asymptotic Behaviour of an Empirical Nearest-Neighbour Distance Function for Stationary Poisson Cluster Processes
Mathematische Nachrichten 136, 131-148 (1988)
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Lothar Heinrich
Asymptotic gaussianity of some estimators for reduced factorial moment measures and product densities of stationary poisson cluster processes
Statistics 19, 87-106 (1988)
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1987
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Lothar Heinrich
A method for the derivation of limit theorems for sums of weakly dependent random variables: a survey
Optimization 18, 715-735 (1987)
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Lothar Heinrich
Asymptotic Expansions in the Central Limit Theorem for a Special Class ofm-Dependent Random Fields. I
Mathematische Nachrichten 134, 83-106 (1987)
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Lothar Heinrich
On the central limit problem for sequences and fields of m-dependent random variables
Wissenschaft / Technische Universität Dresden: Theorie und Praxis 1987, 25-48 (1987)
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Sonderheft "Limit theorems in Probability Theory and Related Topics", Herausgegeben zu Ehren des 70. Jahrestages der Großen Sozialistischen Oktoberrevolution
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Lothar Heinrich
Rates of Convergence in Stable Limit Theorems for Sums of Exponentially Ψ-mixing Random Variables with an Application to Metric Theory of Continued Fractions
Mathematische Nachrichten 131, 149-165 (1987)
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1986
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Lothar Heinrich
Asymptotic normality of a random point field characteristic
Statistics 17, 453-460 (1986)
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Lothar Heinrich
Beiträge zur Summationstheorie von Folgen und Feldern m-abhängiger Zufallsgrößen
(Bergakademie: Freiberg, 1986)
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Zugl. Freiberg, Bergakademie, Habilitationsschrift, 1987
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Lothar Heinrich
Stable Limit Theorems for Sums of Multiply Indexed m-Dependent Random Variables
Mathematische Nachrichten 127, 193-210 (1986)
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1985
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Lothar Heinrich
An elementary proof of spitzer-’s identity
Statistics 16, 249-252 (1985)
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Lothar Heinrich
Non-Uniform Estimates, Moderate and Large Deviations in the Central Limit Theorem form-Dependent Random Variables
Mathematische Nachrichten 121, 107-121 (1985)
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Lothar Heinrich and Volker Schmidt
Normal convergence of multidimensional shot noise and rates of this convergence
Advances in Applied Probability 17, 709-730 (1985)
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Lothar Heinrich
Some Estimates of the Cumulant-Generating Function of a Sum ofm-Dependent Random Vectors and Their Application to Large Deviations
Mathematische Nachrichten 120, 91-101 (1985)
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Lothar Heinrich
Some Remarks on Asymptotic Expansions in the Central Limit Theorem form-Dependent Random Variables
Mathematische Nachrichten 122, 151-155 (1985)
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Lothar Heinrich
Stable limits for sums of m-dependent random variables
Serdica mathematical journal : Serdika matematičesko spisanie : Serdika matematičesko spisanie 11, 189-199 (1985)
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1984
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Lothar Heinrich
Non-Uniform Estimates and Asymptotic Expansions of the Remainder in the Central Limit Theorem form-Dependent Random Variables
Mathematische Nachrichten 115, 7-20 (1984)
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Lothar Heinrich and Wolf-Dieter Richter
On Moderate Deviations of Sums ofm-Dependent Random Vectors
Mathematische Nachrichten 118, 253-263 (1984)
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Lothar Heinrich
On a test of randomness of spatial point patterns
Series Statistics 15, 413-420 (1984)
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Lothar Heinrich and D. Stoyan
On generalized Palm-Chintschin formulae [Russian]
Izvestia Acad. Sci. Armenian SSR, Ser. Mat. 19, 280-287 (1984)
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Lothar Heinrich
Some Estimates of the Concentration Function of Sums of m-Dependent and Markov-Dependent Random Variables
Mathematische Nachrichten 117, 181-191 (1984)
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Lothar Heinrich
Some estimators for the first-order n-fold Palm moment measure and their application to the investigation of dependences in point processes
Elektronische Informationsverarbeitung und Kybernetik : EIK : Journal of information processing and cybernetics : Journal of information processing and cybernetics 20, 244-251 (1984)
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1983
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Lothar Heinrich
A method for the derivation of limit theorems for some classes of dependent random variables
(Wissenschaftliche Sitzungen zur Stochastik: WSS ; 83,05) (Akademie der Wissenschaften der DDR, Zentralinstitut für Mathematik und Mechanik: Berlin, 1983)
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Lothar Heinrich
Integral limit theorems for inhomogeneous Markov chains in case of a stable limit law [in Russian]
Mathematische Nachrichten 114, 227-235 (1983)
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Lothar Heinrich
Über Wahrscheinlichkeiten großer Abweichungen von Summen Markovsch verbundener Zufallsgrößen bei Nichterfüllung der Cramérschen Bedingung
Litovskij matematičeskij sbornik = Lietuvos matematikos rinkinys = Litauische mathematische Abhandlungen 23, 211-223 (1983)
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1982
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Lothar Heinrich
A New Approach to the Summation Theory of Random Variables Connected in a MARKOV Chain
Mathematische Nachrichten 106, 223-234 (1982)
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Lothar Heinrich
A method for the derivation of limit theorems for sums of m-dependent random variables
Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete 60, 501-515 (1982)
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Lothar Heinrich
Factorization of the characteristic function of a sum of dependent random variables
Lithuanian Mathematical Journal 22, 92-100 (1982)
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Lothar Heinrich
Infinitely Divisible Distributions as Limit Laws for Sums of Random Variables Connected in a Markov Chain
Mathematische Nachrichten 107, 103-121 (1982)
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Lothar Heinrich
Über Wahrscheinlichkeiten großer Abweichungen von Summen Markovsch verbundener Zufallsvektoren bei Nichterfüllung der Cramerschen Bedingung
Mathematische Nachrichten 108, 179-196 (1982)
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Lothar Heinrich
Über eine Faktorisierung der charakteristischen Funktion einer Summe von abhängigen Zufallsgrößen
Litovskij matematičeskij sbornik = Lietuvos matematikos rinkinys = Litauische mathematische Abhandlungen 22, 190-202 (1982)
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1980
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V. Nollau and Lothar Heinrich
Ein Kriterium zur direkten Integrierbarkeit reellwertiger Funktionen
Mathematische Nachrichten 95, 149-155 (1980)
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Lothar Heinrich
Integrale Grenzwertsätze für Wahrscheinlichkeiten großer Abweichungen im Falle homogen Markovsch verbundener Zufallsgrößen
Litovskij matematičeskij sbornik = Lietuvos matematikos rinkinys = Litauische mathematische Abhandlungen 20, 193-214 (1980)
BibTeX | RIS
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Lothar Heinrich
Konvergenzaussagen über Summen Markovsch verbundener Zufallsgrößen unter besonderer Berücksichtigung von Wahrscheinlichkeiten großer Abweichungen
(Technische Universität Dresden: Dresden, 1980)
BibTeX | RIS
Zugl. Dresden, Techn. Univ., Diss. A, 1980, Doktorarbeit
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1978
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Lothar Heinrich
Integrale Grenzwertsätze für Wahrscheinlichkeiten großer Abweichungen im Falle homogen und stationär Markovsch verbundener Zufallsgrößen
(Technische Universität Dresden: Dresden, 1978)
BibTeX | RIS
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