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Publikationen


2017
  • Heinrich, L., Pukelsheim, F., Wachtel, V.: The variance of the discrepancy distribution of rounding procedures, and sums of random variables. Metrika 80, No. 3, 363 - 375. [DOI: 10.1007/s00184-017-0609-0] [PDF 995 KB] (an earlier version appeared under the same title as Prepint No. 02/2016, Institut für Mathematik, Universität Augsburg, 15 pages [PDF 367 KB])
  • Bräu, C., Heinrich, L.: Mixing Properties of Poisson cylinder models. Stochastics 89, No. 5, 753 - 765. (Published online: Jan 16, 2016) [DOI: 10.1080/17442508.2016.1276912] [PDF 1406 KB] (an earlier version appeared under the same title as Prepint No. 03/2016, Institut für Mathematik, Universität Augsburg, 17 pages [PDF 696 KB])

2016

  • Heinrich, L.: On the strong Brillinger-mixing property of alpha-determinantal point processes and some applications. Applications of Mathematics 61, No. 4, 443 - 461. [DOI 10.1007/S10492-016-0141-y] [PDF 966 KB] (an earlier version appeared under the same title as Prepint No. 12/2015, Institut für Mathematik, Universität Augsburg, 15 pages [PDF 503 KB])
  • Bräu, C., Heinrich, L.: Multivariate Poisson distributions associated with Boolean models. Metrika 79, No. 6, 749 - 761. (Published online: March 22, 2016) [DOI 10.1007/s00184-016-0576-x] [PDF 654 KB] (an earlier version appeared under the same title as Prepint No. 10/2015, Institut für Mathematik, Universität Augsburg, 15 pages [PDF 690 KB])
  • Heinrich, L., Muche, L.: Some remarks on second-order characteristics of planar Poisson-Voronoi tessellations. Applied Mathematical Sciences 10, No. 27, 1307 - 1320. [DOI 10.12988/ams.2016.63105] [PDF 560 KB]
2015
  • Heinrich, L.: Gaussian limits of empirical multiparameter K-functions of homogeneous Poisson processes and tests for complete spatial randomness. Lithuanian Mathematical Journal 55, No. 1, 72 - 90. [DOI 10.1007/s10986-015-9266-z] [PDF 304 KB] ( an earlier slightly different version with more figures appeared under the same title as Preprint No. 06/2014 Institut für Mathematik, Universität Augsburg, 28 pages,[PDF 1174 KB])
2014
  • Heinrich, L.: Lower and upper bounds for chord power integrals of ellipsoids. Applied Mathematical Sciences 8 , No. 165, 8257 - 8269. [DOI 10.12988/ams.2014.411913] [PDF 825 KB ] ( an extended version appeared under the title "Lower and upper bounds for chord power integrals of ellipsoids" as Preprint No. 07/2014 Institut für Mathematik, Universität Augsburg, 20 pages, [PDF 639 KB])
  • Heinrich, L., Lück, S., Schmidt, V.: Asymptotic goodness-of-fit-tests for the Palm mark distribution of stationary marked point processes with correlated marks. Bernoulli 20 , No. 4, 1673 - 1697. [ DOI 10.3150/31-BEJ523] PDF 324 KB ( an extended version appeared under the title "Asymptotic goodness-of-fit-tests for the Palm mark distribution of stationary marked point processes with correlated marks" as Preprint No. 06/2011 Institut für Mathematik, Universität Augsburg, 35 pages, [PDF 566 KB]).
  • Heinrich, L., Appelt, M.: A stable limit law for recurrence times of the simple symmetric random walk on the two-dimensional integer lattice. Lithuanian Mathematical Journal 54, No. 3, 308 - 322. [ DOI 10.1007/s10986-014-9245-9 ] [PDF 1015 KB]
  • Heinrich, L., Klein, S.: Central limit theorems for empirical product densities of stationary point processes. Statistical Inference of Stochastic Processes 17, No. 2, 121 - 138. [DOI 10.1007/s11203-014-9094-5 ] [PDF 1.050 KB]
  • Heinrich, L., Klein, S., Moser, M.: Empirical mark covariance and product density function of stationary marked point processes - A survey on asymptotic results. Methodology and Computing in Applied Probability 16, No. 2, 283 - 293. (published online: December 11, 2012) [ DOI 10.1007/s11009-012-9314-7 ] [PDF 524 KB]
2013
  • Heinrich, L., Pawlas, Z.: Absolute regularity and Brillinger-mixing of stationary point processes. Lithuanian Mathematical Journal 53, No. 3, 293 - 310. [ DOI 10.1007/s10986-013-9209-5 ] [PDF 248 KB]
  • Heinrich, L., Spiess, M.: Central limit theorems for volume and surface content of stationary Poisson cylinder processes in expanding domains. Advances in Applied Probability 45, No. 2, 312 - 331. [DOI 10.1239/aap/1370870120] [PDF 11.347 KB]
  • Heinrich, L.: Asymptotic Methods in Statistics of Random Point Processes. In: Stochastic Geometry, Spatial Statistics and Random Fields. ed.: E. Spodarev, Lecture Notes in Mathematics 2068, Springer-Verlag, New York, 115-150. [PDF 1856 KB]
2012
  • Heinrich, L., Lück, S., Schmidt, V.: Non-parametric asymptotic statistics for the Palm mark distribution of beta-mixing marked point processes. arXiv : 1205.5044 [math. ST], 33 pages. [PDF 395 KB] (an earlier version appeared under the title "Asymptotic goodness-of-fit-tests for the Palm mark distribution of stationary marked point processes with correlated marks" as Preprint No. 06/2011 Institut für Mathematik, Universität Augsburg, 35 pages, [PDF 566 KB])
  • Heinrich, L.: Some new results on second-order chord power integrals of convex quadrangles. Rendiconti del Circolo Matematico di Palermo Series II, Suppl. 84, 195 - 205. [PDF 411 KB] (an extended version appeared as Preprint No. 22/2011 , Institut für Mathematik, Universität Augsburg, 22 pages, [PDF 560 KB]).
2011
  • Heinrich, L., Klein, S.: 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, No. 4, 359 - 387. [DOI 10.1524/stnd.2011.1094] [PDF 354 KB] (an earlier version appeared under the same title as Preprint No. 17/2010 Institut für Mathematik, Universität Augsburg, 28 pages, [PDF 440 KB])
2010
  • Heinrich, L., Werner, M.: Strongly consistent estimation in Wicksell's corpuscle problem in case of occluded spheres. Advances and Applications in Statistical Sciences 4, No. 2, 89 - 119. [PDF 1604 KB] (an earlier version appeared under the title "Strongly consistent estimation in Wicksell's corpuscle problem in case of unobservable diameters in the intersection plane" as Preprint No. 429 (2000), Institut für Mathematik, Universität Augsburg, 26 pages)
  • Heinrich L., Prokešová M.: On estimating the asymptotic variance of stationary point processes. Methodology and Computing in Applied Probability 12, No. 3, 451 - 471. [DOI 10.1007/s11009-008-9113-3] [PDF 1538 KB] (an earlier version appeared as Thiele Research Report No. 19 October 2006, Department of Mathematical Sciences, University of Aarhus, 23 pages).
2009
  • Heinrich L.: On lower bounds of second-order chord power integrals of convex discs. Rendiconti del Circolo Matematico di Palermo Series II, Suppl. 81, 213 - 222. [PDF 633 KB] (an extended and improved version appeared as Preprint No. 27/2009, Institut für Mathematik, Universität Augsburg, 12 pages, [PDF 756 KB]).
  • Heinrich L.: Central limit theorems for motion-invariant Poisson hyperplanes in expanding convex windows. Rendiconti del Circolo Matematico di Palermo Series II, Suppl. 81, 187 - 212. [PDF 1572 KB] (appeared with an Appendix as Preprint No. 43/2007, Institut für Mathematik, Universität Augsburg, 28 pages, [PDF 518 KB]).
  • Heinrich L., Spiess M.: Berry-Esseen bounds and Cramér-type large deviations for the volume distribution of Poisson cylinder processes. [DOI 10.1007/s10986-009-9061-9] Lithuanian Mathematical Journal 49, No. 4, 381 - 398. [PDF 844 KB]


2008

  • Heinrich L.: On the Miquel point of simplices. Elemente der Mathematik 63, No. 3, 126 - 136. [DOI: 0013-6018/08/030126-11] [PDF 6.398 KB] (for an earlier draft with Maple figures see [PDF 10.524 KB] ).
  • Heinrich L., Muche L.: Second-order properties of the point process of nodes in a stationary Voronoi tessellation. Math. Nachr. 281, No. 3, 350 - 375. [DOI: 10.1002/mana2005106.07] [PDF 984 KB] see in addition [PDF 738] (The first version of this paper with a detailed proof of Lemma 3.1 appeared under the title "On the pair correlation function of the point process of nodes in a Voronoi tessellation" as Preprint No. 94-07 (1994), Fakultät für Mathematik und Informatik, TU Bergakademie Freiberg, 30 pages, [PDF 228 KB] ).
  • Heinrich L., Pawlas Z.: Weak and strong convergence of empirical distribution functions from germ-grain processes. Statistics 42, No. 1, 49 - 65 [DOI: 10.1080/02331880701538532] [PDF 435 KB] (appeared under the title "Asymptotic Properties of Horvitz-Thompson Type Empirical Distribution Functions" as KPMS Preprint No. 36 (2005), Faculty of Mathematics and Physics, Charles University Prague, 27 pages).
 
2007
  • Heinrich L.: Comment in : Discussion of `Modern Statistics for Spatial Point Processes'. Scandinavian Journal of Statististics 34, No. 4, 695 - 696. [DOI: 10.1111/j.1467-9469.2007.00571.x] [PDF 1124 KB]
  • Heinrich L., Schmidt H., Schmidt V.: Limit theorems for functionals on the facets of stationary random tessellations. Bernoulli 13, No. 3, 863 - 891. [DOI: 10.3150/07-BEJ6131] [PDF 305 KB] (last version with corrected typos [PDF 381 KB] )
  • Heinrich L.: Limit distributions of some stereological estimators in Wicksell's corpuscle problem. Image Analysis & Stereology 26, No. 2, 63 - 71. [PDF 1057 KB] (for detailed proofs of the results see [PDF 289 KB])
  • Heinrich L.: An almost-Markov-type mixing condition and large deviations for Boolean models on the line. Acta Applicandae Mathematicae 96, 247 - 262. [DOI: 10.1007/s10440-007-9105-2] [PDF 210 KB]
 
2006
  • Pawlas Z., Heinrich L.: Nonparametric Testing of Distribution Functions in Germ-Grain Models. In: Case Studies in Spatial Point Process Modeling. eds.: A. Baddeley, P. Gregori, J. Mateu, R. Stoica, D. Stoyan, Lecture Notes in Statistics 185, Springer-Verlag, New York, 125-133. [PDF 801 KB]
  • Heinrich L., Schmidt H., Schmidt V.: Central limit theorems for Poisson hyperplane tessellations. Annals of Applied Probability 16, No. 2, 919-950. [DOI: 10.1214/1050516000000033] [PDF 712 KB] , [htt://www.imstat.org/aap/] (appeared also as Preprint No. 456 (2005), Institut für Mathematik, Universität Augsburg, 23 pages.)
  • Heinrich L., Schwingenschlögl U.: Goodness-of-fit criteria for the Adams and Jefferson rounding method and their limiting laws. Metrika 64, 191-207. [DOI: 10.1007/s00184-006-0044-0] [PDF 924 KB]
 
2005
  • Heinrich L.: Large deviations of the empirical volume fraction for stationary Poisson grain models. Annals of Applied Probability 15, No. 1 A, 392-420. [PDF 357 KB] , [PDF 248 KB] , [http://www.imstat.org/aap/] (appeared with supplements under the title "Thermodynamic limit and large deviations of the empirical volume fraction for stationary Poisson grain models" as Preprint No. 425 (2000), Institut für Mathematik, Universität Augsburg, 32 pages, [PDF 383 KB] )
  • Heinrich L., Schmidt H., Schmidt V.: Limit theorems for stationary tessellations with random inner cell structures. Advances in Applied Probability 37, No. 1, 25-47. [PDF 1807 KB] (appeared as Preprint No. 453 (2004), Institut für Mathematik, Universität Augsburg, 24 pages.)
  • Heinrich L., Pukelsheim F., Schwingenschlögl U.: On stationary multiplier methods for the rounding probabilities and the limiting law of the Sainte-Laguë divergence. Statistics & Decisions 23, 117-129. [PDF 1060 KB]
2004
  • Böhm S., Heinrich L., Schmidt V.: Kernel estimation of the spectral density of stationary random closed sets. Australian & New Zealand Journal of Statistics 46, No. 1, 41-51. Festschrift in Honour of Daryl Daley [PDF 841 KB] (an extended version appeared as Preprint No. 447, Institut für Mathematik, Universität Augsburg, 22 pages [PDF 823 KB].)
  • Heinrich L., Pukelsheim F., Schwingenschlögl U.: Sainte-Laguë's chi-square divergence for rounding probabilities and its convergence to a stable law. Statistics & Decisions, 22, 43-59. [PDF 1085 KB] (appeared as Preprint No. 451 (2004), Institut für Mathematik, Universität Augsburg, 12 pages.)
  • Böhm S., Heinrich L., Schmidt, V.: Asymptotic properties of estimators for the volume fractions of jointly stationary random sets. Statistica Neerlandica 58, No. 4, 388-406. [PDF 1239 KB] (appeared as Preprint No. 452 (2004), Institut für Mathematik, Universität Augsburg, 19 pages.)
 
2001
  • Heinrich L.: 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. [PDF 778 KB] (appeared as Preprint No. 433 (2001), Institut für Mathematik, Universität Augsburg, 19 pages.)
 
2000
  • Heinrich L., Werner M.: Kernel estimation of the diameter distribution in Boolean models with spherical grains. Journal of Nonparametric Statistics 12, No. 2, 147-176. [PDF 1411 KB] (appeared as Preprint No. 383 (1998), Institut für Mathematik, Universität Augsburg, 25 pages.)
1999
  • Heinrich L., Molchanov I.S.: Central limit theorem for a class of random measures associated with germ-grain models. Advances in Applied Probability 31, 283-314. [PDF 2281 KB] (an earlier version appeared as Report BS-R9518 June 1995, Dept. of Operations Research)

1998

  • Heinrich L.: On asymptotic estimation in Wicksell's corpuscle problem. Proceedings of Prague Stochastics '98, (Eds.: M. Huskova et al.), Vol. 1, August 23 to 28, 1998, Prague, pp. 227-231.)
  • Heinrich L., Körner R., Mehlhorn N., Muche L.: Numerical and analytical computation of some second-order quantities of spatial Poisson Voronoi tessellations. Statistics 31, No. 2, 231-259. [PDF 1567 KB] (appeared as Preprint No. 96-08, Fakultät für Mathematik und Informatik, TU Bergakademie Freiberg, 28 pp.) Comments: 1. The erronous numerical values on pp. 256/257 have been corrected in the Erratum [PDF 738 KB] 2. An appendix is added which presents recent and more precise numerical results for three non-parametric characteristics connected witth the Poisson-Voronoi tessellation.
  • Heinrich L., Werner M.: A contribution to nonparametric statistics of particle systems. Zeitschrift für Angewandte Mathematik und Mechanik 78, Suppl. 3, 941-942 [PDF 199 KB].
  • Heinrich L.: Contact and chord length distribution of a stationary Voronoi tessellation. Advances of Applied Probability 30, 603-618. [PDF 1135 KB] (appeared as Preprint No. 96-08, Fakultät für Mathematik und Informatik, TU Bergakademie Freiberg, 17 pp.)

1997
  • Heinrich L., Liebscher E.: Strong convergence of kernel estimators for product densities of absolutely regular point processes. Journal of Nonparametric Statistics 8, No. 1, 65-96. [PDF 1474 KB]. (appeared as Preprint No. 96-12, Fakultät für Mathematik und Informatik, TU Bergakademie Freiberg, 17 pp.)
  • Heinrich L.: Absolute regularity of stochastic processes and fields. In: Encyclopaedia of Mathematics, Supplement I, pp. 490-491 (Ed.: M. Hazewinkel), Kluwer Academic Publishers, Dordrecht, [PDF 198].
  • Heinrich L.: Poisson approximation for the number of large digits of inhomogeneous f-expansions. Monatshefte für Mathematik 124, 237-253. [PDF1023 KB].
1996
  • Heinrich L.: Mixing properties and central limit theorem for a class of nonidentical piecewise monotonic C2-transformations. Mathematische Nachrichten 182, 185-214. [PDF 1644 KB] (appeared as Preprint No. 91-025, SFB 343, Universität Bielefeld, 27 pp.)
1995
  • Heinrich L., Schüle E.: Generation of the typical cell in a non-Poissonian Johnson-Mehl tessellation. Communications in Statistics-Stochastic Models 11, No. 3, 541-560. [PDF 1322 KB]
  • Götze F., Heinrich L., Hipp C.: m-dependent random fields with analytic cumulant-generating function. Scandinavian Journal of Statistics 22, No. 2, 183-195. [PDF 940 KB]. (appeared as Preprint No. 91-019, SFB 343, Universität Bielefeld, 16 pp.)
1994
  • Heinrich L., Muche L.: On the pair correlation function of the point process of nodes in a Voronoi tessellation. Preprint No. 94-07, Fakultät für Mathematik und Informatik, TU Bergakademie Freiberg, [PDF 223 KB]
  • Heinrich L., Molchanov I. S.: Some limit theorems for extremal and union shot-noise processes. Mathematische Nachrichten 168, 139-159 [PDF 1377 KB].
  • Heinrich L.: Normal approximation for some mean-value estimates of absolutely regular tessellations. Mathematical Methods of Statistics 3, No. 1, 1-24. [PDF 1363 KB] (appeared as Preprint No. 92-044, SFB 343, Universität Bielefeld, 26 pp.)
1993
  • Heinrich L.: Tail triviality of point processes and Poisson convergence for some classes of particle motions. Preprint No. 93-01, Fachbereich Mathematik, TU Bergakademie Freiberg, 21 pp.
  • Heinrich L., Wolf W.: On the convergence of U-statistics with stable limit distribution. Journal of Multivariate Analysis 44, No. 2, 266-278 [PDF 604 KB].
  • Heinrich L.: Asymptotic properties of minimum contrast estimators for parameters of Boolean models. Metrika 40, No. 2, 67-94. [PD1428 KB]. (appeared as Preprint No. 91-066, SFB 343, Universität Bielefeld, 23 pp.)
1992
  • Heinrich L.: Mixing properties of Gibbsian point processes and asymptotic normality of Takacs-Fiksel estimates. Preprint No. 92-051, SFB 343, Universität Bielefeld, [PDF 2024 KB].
  • Heinrich L.: On the existence and mixing properties of germ-grain models. Statistics 23, No. 2, 271-286. [PDF 1081 KB] (appeared as Preprint No. 91-038, SFB 343, Universität Bielefeld, 20 pp.)
  • Heinrich L.: Bounds for the absolute regularity coefficient of a stationary renewal process. Yokohama Mathematical Journal 40, No. 1, 25-33. [PDF 444 KB]. (appeared as Preprint No.91-068, SFB 343, Universität Bielefeld, 11 pp.)
  • Heinrich L.: Minimum contrast estimates for parameters of spatial ergodic point processes. Transactions of the 11th Prague Conference on Information Theory, Statistical Decision Functions, Random Processes, August 27 to 31, 1990, Prague, pp. 479-492. [PDF 624 KB].
1991
  • Lorz U., Heinrich L.: Normal and Poisson approximation of infinitely divisible distribution functions. statistics 22, No. 4, 627-649. [PDF 1090 KB]
  • Heinrich L.: Goodness-of-fit tests for the second moment function of a stationary multidimensional Poisson process. statistics 22, No. 2, 245-268. [PDF 1571 KB]
1990
  • Heinrich L.: Some bounds of cumulants of m-dependent random fields. Mathematische Nachrichten 149, 303-317. [PDF 848 KB]
  • Heinrich L., Schwandke A.: Some remarks on second-order analysis of planar fibre processes by line intersection. Mathematische Nachrichten 146, 247-257. [PDF 729 KB]
  • Heinrich L.: 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. [PDF 1265 KB]
  • Heinrich L.: Asymptotic expansions in the central limit theorem for a special class of m-dependent random fields II: Lattice case. Mathematische Nachrichten. 145, 309-327. [PDF 1160 KB]
1988
  • Heinrich L., Wolf W.: Uniform and non-uniform approximations of U-statistics by stable distributions. In: Proceedings of the Fourth Prague Symposium on Asymptotic Statistics, Prague, Aug. 29 - Sept. 02, 1988, pp. 249-257. [PDF 375 KB]
  • Heinrich L.: Asymptotic Gaussianity of some estimators for reduced factorial moment measures and product densities for stationary Poisson cluster processes. statistics 19, No. 1, 87-106. [PDF 1580 KB]
  • Heinrich L.: Asymptotic behaviour of an empirical nearest-neighbour distance function for stationary Poisson cluster processes. Mathematische Nachrichten 136, 131-148. [PDF 1141 KB]

1987

  • Heinrich L.: On the central limit problem for sequences and fields of m-dependent random variables. Limit theorems in Probability Theory and Related Topics, TU Dresden, pp. 25-48. [PDF 1251 KB]
  • Heinrich L.: A method for the derivation of limit theorems for some classes of dependent random variables. A survey. optimization 18, No. 5, 715-735. [PDF 1734 KB]
  • Heinrich L.: Asymptotic expansions in the central limit theorem for a special class of m-dependent random fields I. Mathematische Nachrichten 134, 83-106. [PDF 1432 KB]
  • Heinrich L.: Rates of convergence in stable limit theorems for sums of exponentially psi-mixing random variables with an application to the metric theory of continued fractions. Mathematische Nachrichten 131, 149-165. [PDF 1027 KB]
1986
  • Heinrich L.: Asymptotic normality of a point field characteristic in Rd. statistics 17, No. 3, 453-460. [PDF 448]
  • Heinrich L.: Stable limit theorems for sums of multiply indexed m-dependent random variables. Mathematische Nachrichten 127, 193-210. [PDF 1281 KB]
1985
  • Heinrich L., Schmidt V.: Normal convergence of multidimensional shot-noise and rates of this convergence. Advances in Applied Probability 17, No. 4, 709-730. [PDF 1247 KB]
  • Heinrich L.: Stable limits for sums of m-dependent random variables. Serdica (Bulg. Math. Publ.) 11, 189-199. [PDF 881 KB]
  • Heinrich L.: An elementary proof of Spitzer's identity. statistics 16, No. 2, 249-252. [PDF 214 KB]
  • Heinrich L.: Some remarks on asymptotic expansions in the central limit theorem for m-dependent random variables. Mathematische Nachrichten 122, 151-155. [PDF 284 KB]
  • Heinrich L.: Non-uniform estimates, moderate and large deviations in the central limit theorem for m-dependent random variables. Mathematische Nachrichten 121, 107-121. [PDF 911 KB]
  • Heinrich L.: Some estimates of the cumulant-generating function of a sum of m-dependent random vectors and their application to large deviations. Mathematische Nachrichten 120, 91-101.[PDF 940 KB]
1984
  • Heinrich L., Stoyan D.: On generalized Palm-Chintschin formulae. (Russian) Izvestia Acad. Sci. Armenian SSR, Ser. Mat. XIX, No. 4, 280-287. [PDF 416 KB]
  • Heinrich L.: Some estimators for the first-order n-fold Palm moment measure and their application to the investigation of dependences in point processes. Elektronische Informationsverareitung und Kybernetik (J. Information Processing and Cybernetics) 20, No. 5/6, 244-251. [PDF 661 KB]
  • Heinrich L.: On a test of randomness of spatial point patterns. Mathematische  Operationsforschung und Statististik, Ser. statistics 15, No. 3, 413-420. [PDF 538 KB]
  • Heinrich L., Richter W.-D.: On moderate deviations of sums of m-dependent random vektors. Mathematische Nachrichten 118, 253-263. [PDF 703 KB]
  • Heinrich L.: Some estimates of the concentration function of sums of m-dependent and Markov-dependent random variables. Mathematische Nachrichten 117, 181-191. [PDF 653 KB]
  • Heinrich L.: Non-uniform and asymptotic expansions of the remainder in the central limit theorem for m-dependent random variables. Mathematische Nachrichten 115, 7-20. [PDF 682 KB]
1983
  • Heinrich L.: A method for the derivation of limit theorems for some classes of dependent random variables. Wiss. Sitzungen zur Stochastik 05/83, Institut für Mathematik der AdW der DDR.
  • Heinrich L.: Integral limit theorems for inhomogeneous Markov chains in case of a stable limit law. (Russian) Mathematische Nachrichten 114, 227-235. [PDF 531 KB]
  • Heinrich L.: Über Wahrscheinlichkeiten großer Abweichungen von Summen Markovsch verbundener Zufallsgrößen bei Nichterfüllung der Cramérschen Bedingung. Liet. Matem. Rinkinys 23, No. 1, 211-223. [PDF 774 KB]
1982
  • Heinrich L.: A method for the derivation of limit theorems for sums of m-dependent random variables. Z. Wahrscheinlichkeitstheorie verw. Gebiete 60, 501-515. [PDF 519 KB]
  • Heinrich L.: Über Wahrscheinlichkeiten großer Abweichungen von Summen Markovsch verbundener Zufallsvektoren bei Nichterfüllung der Cramérschen Bedingung. Mathematische Nachrichten 108, 179-196. [PDF 1184 KB]
  • Heinrich L.: Infinitely divisible distributions as limit laws for sums of random variables connected in a Markov chain. Mathematische Nachrichten 107, 103-121. [PDF 772 KB]
  • Heinrich L.: A new approach to the summation theory of random variables connected in a Markov chain. Mathematische Nachrichten 106, 223-234. [PDF 776 KB]
  • Heinrich L.: Über eine Faktorisierung der charakteristischen Funktion einer Summe von abhängigen Zufallsgrößen. Liet. Matem. Rinkinys 22, No. 1, 190-202. [PDF 997 KB] English translation: Factorization of the characteristic function of a sum of dependent random variables. Lithuanian Mathematical Journal 22, No. 1, 92-100. [PDF 597 KB]
1980
  • Heinrich L.: Integrale Grenzwertsätze für Wahrscheinlichkeiten großer Abweichungen im Falle homogen Markovsch verbundener Zufallsgrößen. Liet. Matem. Rinkinys 20, No. 1, 193-214 [PDF 1365 KB]
  • Heinrich L., Nollau V.: Ein Kriterium zur direkten Integrierbarkeit reellwertiger Funktionen. Mathematische Nachrichten 95, 149-155. [PDF 351 KB]

Diploma thesis

Integrale Grenzwertsätze für Wahrscheinlichkeiten großer  Abweichungen im Falle homogen und stationär Markovsch verbundener Zufallsgrößen

Integral limit theorems for probabilities of large deviations of random variables connected in a homogeneous and stationary Markov     chain (English title)

Referees: Prof. Dr. Werner Wolf (supervisor), Doz. Dr. Rolf Kühne (both  Technical Unversity of Dresden), defended on January 30, 1978


Doctoral thesis 

Konvergenzaussagen über Summen Markovsch verbundener Zufallsgrößen unter besonderer Berücksichtigung von Wahrscheinlichkeiten großer Abweichungen

Convergence of sums of random variables connected in a Markov chain  with particular focus on probabilities of large deviations (English title)

Referees: Prof. Dr. Werner Wolf (supervisor, Technical University of Dresden),  Prof. Dr. Dieter König (Mining Academy of Freiberg), Dr. Leonas Saulis (State University of Vilnius), defended at Technical University of Dresden on November 27, 1980


Habilitation thesis

Beiträge zur Summationstheorie von Folgen und Feldern m-abhängiger Zufallsgrößen

Contributions to the theory of sums of sequences and fields of m-dependent random variables (English title)

Referees: Prof. Dr. Dieter König  (Mining Academy of Freiberg),  Prof. Dr. Werner Wolf, (Technical University of Dresden),  Prof. Dr. Friedrich Liese (University of Rostock), defended at Mining Academy of Freiberg on May 14, 1987