ISSN 1002-1027　　CN 11-2952/G2

### Law of Iterated Logarithms of MLE for Non-homogeneous Poisson Processes

FANG Xiangzhong

1. School of Mathematical Sciences, Peking University, Beijing, 100871
• Received:1997-04-25 Online:1998-09-20 Published:1998-09-20

Abstract: This paper study the law of iterated logarithms of maximum likelihood estimate for general non-homogeneous Poisson processes. Suppose{N(t), t≥0} is a Poisson process on probability space{Ω, F, Pθ}, where θ=(θ1,...,θm) is unknown parameter. Let θ=(θ1,...,θm) be the true value of θ, θ(T)=(θ1(T),...,θm(T)) be the MLE of θ and (aij)i,j=1,...,m the inverse martrix of the information matrix, then under some conditions, for any i(1≤im), the following equation hold