Semi-stable Markov processes in rn

Sun-Wah Kiu

Stochastic Processes and their Applications, 1980, vol. 10, issue 2, 183-191

Abstract: A Markov process in Rn{xt} with transition function Pt is called semi-stable of order [alpha]>0 if for every a>0, Pt(x, E) = Pat(aax, aaE). Let [phi]t([omega])=[integral operator]t0xs([omega])-1/[alpha] ds, T(t) be its inverse and {yt}={xT(t)}. Theorem 1: {Yt} is a multiplicative invariant process; i.e., it has transition function qt satisfying qt(x,E)=qt(ax,aE) for all a > 0. Theorem 2: If {xt} is Feller, right continuous and uniformly stochastic continuous on a neighborhood of the origin, then {yt} is Feller.

Date: 1980
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