%0 Journal Article %A WANG Huaming %T Limit Theorems for Birth and Death Process with One-Side Bounded Jumps in Random Environment %D 2019 %R 10.3969/j.issn.1001-4268.2019.01.004 %J CHINESE JOURNAL OF APPLIED PROBABILITY AND STATISTICS %P 51-62 %V 35 %N 1 %X

We study a birth and death process $\{N_t\}_{t\ge0}$ in i.i.d. random environment, for which at each discontinuity, one particle might be born or at most $L$ particles might be dead. Along with investigating the existence and the recurrence criterion, we also study the law of large numbers of $\{N_t\}$. We show
that the first passage time can be written as a functional of an $L$-type branching process in random environment and a sequence of independent and exponentially distributed random variables. Consequently, an explicit velocity of the law of large numbers can be given.

%U http://aps.ecnu.edu.cn/EN/10.3969/j.issn.1001-4268.2019.01.004