μ-invariant Measures Of Jump Process

As is known to all,μ-invariant measure plays an important role in stochastic pro-cess,and the research of that is significant both in theory and practice.In this paper,we concentrate on studying theμ-invariant measure of jump process.Firstly,we prove an ex-istence theorem for jump process containing one instantaneous state.Then,we discuss the question that when there is a q-process P(t),such thatπwhich is theμ-invariant measure orμ-subinvariant measure of a given q-pair,is theμ-invariant measure of P(t).This thesis is composed of three chapters;In the first chapter,we simply introduce some basic concepts,which include translation function,q-pair,q-process,forback equation,forward equation,q-resolvent function and so Oil.In the second chapter,we firstly recall the existence theorem for jump process(total Stable),and prove an existence theorem for jump process containing one instantaneous state.In the third chapter,we discuss the question that when there is a q-process P(t),such thatπwhich is theμ-invariant measure orμ-subinvariant measure of a given q-pair,is theμ-invariant measure of P(t)in three conditions.