论文信息 - Reduced critical branching processes in random environment

Reduced critical branching processes in random environment

Let Z(n), N = 0, 1, 2, ... be a critical branching process in random environment and Z(m, n), m 0 converges to a non-trivial limit as n --> [infinity]. We also prove the convergence of the conditional distribution of the process {n-1/2 log Z([nt], n), 0 0 to the law of a transformation of the Brownian meander. Some applications of the above results to random walks in random environment are indicated.

Vladimir Vatutin | Konstantin Borovkov | K. Borovkov | V. Vatutin

[1] D. Iglehart. Functional Central Limit Theorems for Random Walks Conditioned to Stay Positive , 1974 .

[2] A local limit theorem for first passage time , 1979 .

[3] Walter L. Smith,et al. On Branching Processes in Random Environments , 1969 .

[4] S. Sagitov. Three limit theorems for reduced critical branching processes , 1995 .

[5] Alan Agresti,et al. On the extinction times of varying and random environment branching processes , 1975, Journal of Applied Probability.

[6] A. M. Zubkov. Limiting Distributions of the Distance to the Closest Common Ancestor , 1976 .

[7] Erwin Bolthausen,et al. On a Functional Central Limit Theorem for Random Walks Conditioned to Stay Positive , 1976 .

[8] K. Fleischmann,et al. Subkritische räumlich homogene Verzweigungsprozesse , 1975 .

[9] Klaus Fleischmann,et al. The Structure of Reduced Critical GALTON‐WATSON Processes , 1977 .

[10] M. V. Kozlov,et al. On the Asymptotic Behavior of the Probability of Non-Extinction for Critical Branching Processes in a Random Environment , 1977 .

[11] Vladimir Vatutin,et al. Branching processes. II , 1993 .