Absolute Continuity of Markov Processes and Generators

Abstract

Let (x, ζ,ℬ t ,P x ) be a (standard) Markov process with state space 5 defined on the abstract space Ω. Here, x t is the sample path, ζ is the terminal time and ℬ t is the smallest α-field of Ω in which x s s ≤ t are measurable. Let P’ x , x ∈ S be another family of Markovian measures defined on (ℬ t , Ω).