Excursions of Markov Processes (Probability and its Applications)

Discusses the analysis and construction of Markov processes in terms of the excursions of the path between visits to a subset of the state space. Its purpose is to attract graduate students and research mathematicians to the subject (and to probabilistic potential theory in general) and to acquaint them with the theory, techniques and applications of the excursion viewpoint. The book's emphasis is on a notable aspect of excursion theory - its use in making specific computations and in providing concrete illustrations of many of the concepts, even some deeply theoretical ones, from probabilistic potential theory. Because of this feature of excursion theory and the book's emphasis on examples and specific applications of general Markov processes and probabilistic potential theory. There is much current research in probability that uses the ideas and techniques of excursion theory; and many open problems are suggested by this research. The present book gives a development of the theoretical background complete enough to allow readers to understand current research and start working on projects of their own.