A REGULARIZATION RESULT OF THE CONTINUOUS PMC MARKOV SEMIGROUPS

BERTOGLIO, N; DARTNELL, P; MARTINEZ, S; MARTIN, JS

A REGULARIZATION RESULT OF THE CONTINUOUS PMC MARKOV SEMIGROUPS

Date

1991

Authors

Abstract

Let (W(t))t is-an-element-of R+ be the PMC Markov semigroup and assume usual regular conditions on the probability space (X, Beta, mu). We show that there exist a class of mu-preserving transition kernels (Q(t))t is-an-element-of R+ and a full mu-measure set X approximately such that the action of Q(t) on L2 (mu) is given by W(t), and the semigroup equality Q(t)Q(s)f(x) = Q(t + s)f(x) is verified for any bounded measurable function f, for any x is-an-element-of X approximately and for any t, s is-an-element-of R+.