Excursions Away From a Set

Abstract

Part of the theory of excursions away from a point can be generalized as follows. Let {X _t ; t ≥ 0} be a standard process and let V be a subset of the state space E. We will assume that V is closed and that every point of V is regular for V, that is P^x(σ = 0) = 1 for all x in V where σ = σ _v = inf{t > 0|X _t ∈ V}. As in Chapter III let G = G(ω) denote the strictly positive left ends of the open intervals making up the complement of the closure of {t|X _t (ω) ∈ V}.