On some Asymptotic Properties of Markoff Processes

Let (Q, F) be a measurable space and (1.1) P(x, E; t) = Pr[X(t+s) ∈ E/X(s)=x], x ∈Ω, E ∈ F, t > 0, be the transition probability for a Markoff Process X(t), t > 0, X(0)=x₀ with values in Ω. P(x, E; t) is a measure over F for fixed x, t and for each E is a measurable function in (x, t).