Reduced critical branching processes in random environment

K. A. Borovkov and V. A. Vatutin

Stochastic Processes and their Applications, 1997, vol. 71, issue 2, 225-240

Abstract: 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.

Keywords: 60J80; 60J15; 60F17; Branching; process; in; random; environment; Reduced; process; Conditional; limit; theorem; Brownian; meander (search for similar items in EconPapers)
Date: 1997
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