On Bayes’ Formula for Doubly Stochastic Point Process on the Real Half-Line

Abstract

We consider a marked point process Ф on the real half-line, a random element Z and the filtration {?} generated by Z and the restriction Фt of Ф up to, In these notes we deal with the (filtering) problem of determining the conditional distribution P(Z ? ·|Фt) using certain {?}intensities of Ф, We prove Bayes' formula and illustrate its role in the framework of our assumption on the filtration {?}, Some results of the literature will be generalized