On Representation of Excessive Measures for S-Subordinated Markov Processes

摘要

Let X and Y be two transient Markov processes defined on a common state space such that Y is S-subordinated to X, i.e. each X-excessive function is Y-excessive. Based on a classical representation of excessive measures and a projection result established recently, we prove that, for each Y-excessive m, there exists a unique X-entrance law (nu(t)) such thatmP(t) = m(i) + nu V-t; t 0where (P-t) is the transition function of X, m(i) is the Y-invariant part of m and V is the potential kernel of Y. Moreover, some applications of this result are derived.