Statistical inference for inhomogeneous spatial Markov point processes

本文主要研究空间点过程的TIM模型，并研究了模型参数的极大似然估计的渐近性态。本文研究了极大似然估计的相合性和渐近正态性在什么条件下是成立的。齐次空间过程的遍历定理和中心极限定理是我们问题的关键。但是这些定理不能直接应用。因此，我们讨论了定理的适用性。不幸的是，我们没有给出精确的条件，需要进一步的研究。

In this research, we focused on TIM models for spatial point processes and studied asymptotic behavior of maximum likelihood estimators for model parameters. The purpose of this study is to investigate under which conditions consistency and asymptotic normality of the maximum likelihood estimators are assured. Ergodic theorems and central limit theorems for homogeneous spatial processes are keys for our problems. But these theorems cannot be applied directly. Therefore we discussed the applicability of the theorems. Unfortunately we failed to give precise conditions and further research will be needed.