两参数Poisson过程的鞅刻画

On the Martingale Description of Two-parameter Poisson Process

本文给出了两参数Poisson过程的鞅刻画并讨论了这种过程的强Markov性。两参数随机过程(P_为Poisson过程的充要条件是(N_)=(P_-st)为鞅;设(P_)为Poisson过程,则(P_~T)=(P(]T,T+z]))仍为Poisson过程且P_~T与F_T~*独立,其中,T为有限弱停点,z=(s,t)∈R_+~2,F_~*=F_~*∨F_~2。

In this paper the martingale description of two-parameter Poisson process is given and the strong Markov property of this process is discussed, The main result is that two-parameter stochastic process (P_) is a poisson process, iff(N_)=(P_-st) is a martingale; if (P_)is a poisson process, then(P_~T)= (P(]T,T+z])) is also poisson process, and p_~T and are independent,where T is a finite weak stopping point z=(s,t) ∈R_+F_2~#=F_2~1∨F_~2.