ABSTRACT
This chapter focuses not on inference for other stochastic processes given observations resulting from a point process sampling mechanism. It examines only Markov processes, stationary processes on R and stationary random fields, and only Poisson process samples. The chapter utilizes marked point processes to unify the problem formulation, but this produces a coherent statement, not broadly applicable methods. It also focuses on Poisson sampling of stochastic processes. Regular sampling has been studied for birth processes or death processes, binary Markov processes, and stationary processes. By contrast, Poisson sampling has been known at least since Shapiro and Silverman to be alias-free for a very broad class of stationary processes. The chapter examines Poisson sampling of stationary stochastic processes on R. It deals with analysis of combined statistical inference and state estimation.
