The Theory Of Excursion Of Markov Chains

In the theory of Markov processes,the theory of excursion is a strong tool to describe the construction of the sample paths of Markov processes.So in this case,the sample paths of processes should be right-continuous and have left-limit,however Markov chains which have instantaneous points don't have this property.So in order to study the construction of the sample paths of Markov chains which have instantaneous points,in this text I establish the theory of excursions of Markov chains.Here is a short description of the content. Section one is a preliminary,which is devoted to the study of Q matrix,Q processes and pseudo Q-matrix.Section two is the excursion theory of Markov chains.In this section,I first describe the local time and inverse local time of Markov chains {X_t}t≥0 at 0, then I introduce the concepts of excursion and excursion measure,and the text reflects the relation among excursion measure, Q-matrix and minimal process.