Sur quelques théorèmes de convergence du processus de naissance avec interaction des voisins

Zhi-Ying Wen

Bulletin de la Société Mathématique de France (1986)

  • Volume: 114, page 403-429
  • ISSN: 0037-9484

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Wen, Zhi-Ying. "Sur quelques théorèmes de convergence du processus de naissance avec interaction des voisins." Bulletin de la Société Mathématique de France 114 (1986): 403-429. <http://eudml.org/doc/87519>.

@article{Wen1986,
author = {Wen, Zhi-Ying},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Galton-Watson process; m-dependent random variables; central limit theorem; law of the iterated logarithm},
language = {fre},
pages = {403-429},
publisher = {Société mathématique de France},
title = {Sur quelques théorèmes de convergence du processus de naissance avec interaction des voisins},
url = {http://eudml.org/doc/87519},
volume = {114},
year = {1986},
}

TY - JOUR
AU - Wen, Zhi-Ying
TI - Sur quelques théorèmes de convergence du processus de naissance avec interaction des voisins
JO - Bulletin de la Société Mathématique de France
PY - 1986
PB - Société mathématique de France
VL - 114
SP - 403
EP - 429
LA - fre
KW - Galton-Watson process; m-dependent random variables; central limit theorem; law of the iterated logarithm
UR - http://eudml.org/doc/87519
ER -

References

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  1. [1] ASMUSEEN (S.). — Some martingale methods in the limit theory of supercritical branching processes, Advance in Probability and Related Topics, vol. 5, 1976, p. 1-26. Zbl0402.60083MR80d:60103
  2. [2] ASMUSEEN (S.). — Almost sure behavior of linear functions of supercritical branching processes, Trans. Americqn Math., vol. 1, 1977, p. 233-248. Zbl0376.60083
  3. [3] ATHREYA (K. B.) and NEY (P. E.). — Branching processes, Springer, New York, 1972. Zbl0259.60002MR51 #9242
  4. [4] BILLINGSLEY. — Probability and mesure, J. Wiley and Sons, 1965. 
  5. [5] HARRIS (T. E.). — The theory of branching processes, Berlin, Springer, 1963. Zbl0117.13002MR29 #664
  6. [6] HEYDE (C. C.) and BROWN (B. M.). — An invariance principle and some convergence rate results for branching processes, Z.W. 1971, p. 270-278. Zbl0212.49505MR46 #10085
  7. [7] HEYDE (C. C.). — Some central limit analogues for supercritical Galton-Watson processes, J. appl. Prob., vol. 8, 1971, p. 52-59. Zbl0222.60054MR43 #8133
  8. [8] HEYDE (C. C.). — Some almost sure convergence theorem for branching processes, Z.W., vol. 20, 1971, p. 189-192. Zbl0212.19703MR47 #5973
  9. [9] NEVEU (J.). — Bases mathématiques du calcul des probabilités, Masson, Paris, 1970. Zbl0203.49901MR42 #6885
  10. [10] PEYRIÈRE (J.). — Mandelbrot random beadsets and birth processes with interaction, I.B.M. Research report, RC-7417. 
  11. [11] PEYRIÈRE (J.). — Processus de naissance avec interaction des voisins, C.R. Acad. Sc., Paris, t. 289, 1979, p. 223-224 et 557. Zbl0414.60070MR80i:60120
  12. [12] PEYRIÈRE (J.). — Processus de naissance avec interactions voisins, évolution de graphes, Ann. Inst. Fourier, vol. 31, 1981. Zbl0452.60089MR84d:60126
  13. [13] SHERGIN (V. V.). — On the convergence rate in the central limit theorem for m-dependent random variables, Theory Prob. Appl., vol. 24, 1979, p. 782-796. Zbl0447.60023MR81e:60024
  14. [14] DOOB (J. L.). — Stochastic processes, J. L. Doob, Wiley, New York, 1953. Zbl0053.26802MR15,445b

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