随机环境中受控分枝过程的稳定性_英文_.pdfVIP

Vol. 29(2009) No.3 J.of Math.(PRC) STABILITY OF CONTROLLED BRANCHING CHAINS * IN RANDOM ENVIRONMENT 1 2 WANG We-i gang , U D-i he (1. School of Statistics and Math. of Zhej iang Gongshang University , H angzhou 310018, China) ( 2. School of Math. and Statistics, Wuhan University, Wuhan 430072, China) Abstract: We consider controlled branching chains in random environments, that the controlled functions are i.i. d. random variables and the reproduction of an individual in then-th season depends on the environments. Some results on process stability are shown. The extinction probabilities are given when environments are stationary and ergodic. Key words: controlled branching chains in random environments; stability; extinction probability 000 MR Subject Classification: 60F15; 60J80 Document code: A Article ID: 0 55-7797( 009)03-0 37-05 1 Introduction The Galton-Watson branching chain is a basic stochastic model for a population of particles developing in time .This model has been generalized to various branching models such as the population-size-dependent branching chain, where the law of offspring distribution depends on thepopulation size, which was considered in [ 1-4] . u [5] studied the existence of the canonicalbranching chain in random environment . Wang and Fang [6-8] studied the population-size-dependent branching chains in random environments when the environments areindependent,stationary or Markov