Simulations and a conditional limit theorem for intermediately subcritical branching processes in random environment

被引:0
作者
Christian Böinghoff
Götz Kersting
机构
[1] Goethe-Universität,Fachbereich Mathematik
来源
Proceedings of the Steklov Institute of Mathematics | 2013年 / 282卷
关键词
Random Walk; Limit Theorem; STEKLOV Institute; Random Environment; Simple Random Walk;
D O I
暂无
中图分类号
学科分类号
摘要
Intermediately subcritical branching processes in random environment are at the borderline between two subcritical regimes and exhibit particularly rich behavior. In this paper, we prove a functional limit theorem for these processes. It is discussed together with two other recently proved limit theorems for the intermediately subcritical case and illustrated by several computer simulations.
引用
收藏
页码:45 / 61
页数:16
相关论文
共 30 条
  • [1] Afanasyev V I(2001)Limit theorems for intermediately subcritical and strongly subcritical branching processes in a random environment Dikret. Mat. 13 132-157
  • [2] Afanasyev V I(2012)Limit theorems for weakly subcritical branching processes in random environment J. Theor. Probab. 25 703-732
  • [3] Böinghoff Ch(2005)Criticality for branching processes in random environment Ann. Probab. 33 645-673
  • [4] Kersting G(2005)Functional limit theorems for strongly subcritical branching processes in random environment Stoch. Processes Appl. 115 1658-1676
  • [5] Vatutin V A(1975)On the extinction times of varying and random environment branching processes J. Appl. Probab. 12 39-46
  • [6] Afanasyev V I(1971)On branching processes with random environments. I: Extinction probabilities Ann.Math. Stat. 42 1499-1520
  • [7] Geiger J(1988)On the survival probability of a branching process in a finite state i.i.d. environment Stoch. Processes Appl. 27 151-157
  • [8] Kersting G(1999)Elementary new proofs of classical limit theorems for Galton-Watson processes J. Appl. Probab. 36 301-309
  • [9] Vatutin V A(2003)Limit theorems for subcritical branching processes in random environment Ann. Inst. Henri Poincaré, Probab. Stat. 39 593-620
  • [10] Afanasyev V I(2001)Propriétés asymptotiques des processus de branchement en environnement aléatoire C. R. Acad. Sci. Paris, Ser. 1: Math. 332 339-344