随机过程的广义收敛性

The Generalized Convergence of a Stochastic Process

给出了一个随机过程{Xt}依概率收敛的充要条件,同时也证明了与{Xt}同极限的几乎处处收敛的随机过程{Yt}也有相同的结论.因此在很多情况下,人们将{Yt}化为{Xt}来研究{Yt}的收敛性;而在其他情况下(除了假设{Xt}与{Yt}是a.s.等价外),人们就要研究{Yt}的一个序列的收敛性.此种处理方法为处理大量旧的与新的分支过程提供了一个一致逼近的途径.

In this paper, a necessary and sufficient condition is given for the convergence in probability of a stochastic process and the almost sure convergence of a stochastic process is discussed too. The method mentioned can be applied to a number of old and new cases of branching processes.