可数状态密度相依生灭过程的大偏差

LARGE DEVIATION FOR DENSITY-DEPENDENT BIRTH-DEATH PROCESS ON COUNTABLE STATE SPACE

本文主要考察可数状态密度相依生灭过程XN,且令∏ N 为 [0 ,∞ ]上XN/N的唯一平稳分布 ,通常这种分布弱收敛到一个退化分布 (N ∞ ) ;

This paper considers a density-dependent birth-death process X N on a countable state space .Let ∏ N be the unique stationary distribution(on [0,∞])of X N. Typically,these distributions converge weakly to a degenerate distribution as N∞. Large deviation is concerned for obtaining the exponential decay rate of these probabilities.