非齐次泊松过程中向量参数极大似然估计的重对数律

对于具有向量参数的非齐次泊松过程的一般模型，论证了向量参数极大似然估计每个分量的收敛速度符合重对数律。

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

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,...,θ_m) is unknown parameter. Let θ^﹡=(θ₁^﹡,...,θ_m^﹡) be the true value of θ, θ^＾(T)=(θ₁^＾(T),...,θ_m^＾(T)) be the MLE of θ and (a_ij)_i,j=1,...,m the inverse martrix of the information matrix, then under some conditions, for any i(1≤i≤m), the following equation hold