Energy functional and killing transform

摘要

LET X = (X_t, P~x) be a right Markov process with state space (E, epsilon), semigroup (P_t) and resolvent ( U~q). As in ref. [1, 2], we denote by Exc~q ( X), Dis~q (X) and Con~q (X) the cones of excessive, dissipative, conservative measures of X, respectively, and by S~q (X) the cone of excessive functions of X. By convention we drop the superscript q when it is zero. Let MF be the set of all exact multiplicative functional of X.. For any given M G MF, write E_M: = {x EUR E: P~x (M_0 = 1) = 1} and S_