Exact convergence rates in Erdös-Rényi type theorems for renewal processes

Jean-Noël Bacro; Paul Deheuvels; Josef Steinebach

Annales de l'I.H.P. Probabilités et statistiques (1987)

  • Volume: 23, Issue: 2, page 195-207
  • ISSN: 0246-0203

How to cite

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Bacro, Jean-Noël, Deheuvels, Paul, and Steinebach, Josef. "Exact convergence rates in Erdös-Rényi type theorems for renewal processes." Annales de l'I.H.P. Probabilités et statistiques 23.2 (1987): 195-207. <http://eudml.org/doc/77297>.

@article{Bacro1987,
author = {Bacro, Jean-Noël, Deheuvels, Paul, Steinebach, Josef},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {renewal processes; Erdős-Renyi laws; almost sure convergence; increments of partial sums},
language = {eng},
number = {2},
pages = {195-207},
publisher = {Gauthier-Villars},
title = {Exact convergence rates in Erdös-Rényi type theorems for renewal processes},
url = {http://eudml.org/doc/77297},
volume = {23},
year = {1987},
}

TY - JOUR
AU - Bacro, Jean-Noël
AU - Deheuvels, Paul
AU - Steinebach, Josef
TI - Exact convergence rates in Erdös-Rényi type theorems for renewal processes
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1987
PB - Gauthier-Villars
VL - 23
IS - 2
SP - 195
EP - 207
LA - eng
KW - renewal processes; Erdős-Renyi laws; almost sure convergence; increments of partial sums
UR - http://eudml.org/doc/77297
ER -

References

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  1. [1] J.N. Bacro, Encadrements limites de la statistique de Shepp. Tech. Rep. 86-45, L. S. T. A., Université Paris-VI, Publ. Inst. Univ. Paris, 1986, 2-3, 1-14. Zbl0667.60034MR899239
  2. [2] P. Deheuvels, On the Erdös-Rényi theorem for random fields and sequences and its relationships with the theory of runs and spacings. Z. Wahrsch. verw. Gebiete, t. 70, 1985, p. 91-115. Zbl0548.60027MR795790
  3. [3] P. Deheuvels and L. Devroye, Limit laws related to the Erdös-Rényi theorem. Tech. Rep. 83-6, L. S. T. A., Université Paris VI. Zbl0637.60039
  4. [4] P. Deheuvels, L. Devroye and J. Lynch, Exact convergence rate in the limit theorems of Erdös-Rényï and Shepp. Ann. Probab., t. 14, p. 209-223. Zbl0595.60033MR815966
  5. [5] M. Retka, Gesetze von Erdös-Rényi-Typ bei Erneuerungsprozessen. Diplomarbeit, Universität Marburg. 
  6. [6] J. Steinebach, Between invariance principles and Erdös-Rényi laws. Coll. Math. Soc. Janos Bolyai, t. 36, 1982, p. 981-1005, Limit Theorems in Probability and Statistics, P. Révész ed., Elsevier, Amsterdam. Zbl0578.60025MR807593
  7. [7] J. Steinebach, Improved Erdös-Rényi and strong approximation laws for increments of renewal processes. Ann. Probab., t. 14, 547-559. Zbl0601.60029MR832023

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