Some Properties of Invariant Functions of Markov Processes

Abstract

Let X = (Ω, F, F_t, X_t, θ_t, P^x) be a right process on a Lusin topological state space E with Borel field B. A point Δ ∈ E will serve as cemetery point. Let P_t and U^a denote the semigroup and resolvent of X. We suppose X is a Borel right process; in particular, U^a f ∈ B⁺ whenever f ∈ B⁺. We restrict our attention to transient Borel right processes throughout this paper, so there is a strictly positive B-measurable function q so that Uq ≤ 1.