STOPPING TIME CHANGES OF TIME HOMOGENEOUS MARKOV PRCOESSES (II)
Liu L · 1986
Let X=(Ω,X_t,θ_t,P~x,T)be a time homogeneous Markov process with state space(E_Δ,)and τ=(τ_t)be anstopping time change(i.e.each τ_t is an stopping time and“s≥tτ_s≥τ_t”).Then X~τ=(Ω,X_(τ_(t)),θ_(τ_(L)),P~x,T)is called a τ-transformation of X.This paper makes a systematic study of invariant properties of Markev processes by stopping time changes.General stopping time changes of general Markov processes are considered and various conditions are given,under which the new process X~τ preserves corresponding properties(e.g.Markov property,strong Markov property,strong Feller property,normal property,complete property and standard property etc.)of the original process X.