连续时间分支过程的一类推广

An Extended Class of Time-Continuous Branching Processes

Chen R R(1 997)对连续时间分支过程进行了推广 ,其 q-矩阵为 (1 .1 ) .对这类 q-矩阵 ,她得到了过程的唯一性准则 ,常返性和正常返性 (即遍历 )的条件 . L in,Zhang和Hou(1 999)对转移函数的性质进行了讨论 ,得到了转移函数是随机单调的 ,强遍历 ,多项式一致收敛 ,指数遍历和 Feller转移函数的条件 .在 Chen R R(1 997)和 L in,Zhang和Hou(1 999)基础上 ,本文对连续时间分支过程的推广进行了进一步的讨论 ,得到了过程的鞅性 。

Chen R R(1997)studied the extended class of time continuous branching processes with q  matrix as (1.1).The uniqueness,recurrence and positive recurrence(that is ,ergodicity) criteria for the processes are presented in her paper.Lin,Zhang and Hou(1999)made a study of the property of transition function and obtained the conditions of transition function which is stochastically monotone,strongly ergodic,polynomial uniformly convergent,exponentially ergodic and Feller transition function.On the basis of the papers of Chen R R(1997) and Lin,Zhang and Hou(1999),we make a further study of the extended class of continuous time branching processes,we obtain the martingale property of the process.In the meantime ,we obtain the condition of the upper estimate of large deviations holds.