Introduction

Abstract

In 1957, G. A. Hunt introduced and developed the potential theory of Markov processes in his fundamental treatise [92]. Hunt’fs theory is essentially based on the fact that the integral of the transition probability of a Markov process defines a potential kernel:

$$U(x, y) = \int_{0}^{\infty} p(t, x, y)dt.$$

One of the important topics in the theory is the study of multiplicative functionals of theMarkov process, corresponding either to SchröNodinger perturbations of the generator of the process, or to killing the process at certain stopping times. Among the most influential treatises on this subject are the monographs [23] by R. M. Blumenthal and R. K. Getoor, [60] by K. L. Chung, [22] by W. Hansen and J. Bliedtner, and [62] by K. L. Chung and Z. Zhao.