The Duality Methods Of Markov Processes And Their Applications

Duality is a very common and important concept in modern mathematics. Itis applied in almost every branch of mathematics. The main aim of the thesis isto study duality methods of Markov process. We discuss three kinds of duality indetail, that is, monotone duality, moment duality and Laplace duality.In the first chapter, We introduce the research background, the research status,the research significance of duality. Then we give the main research results of thisthesis.In the second chapter, we introduce basic theory related to the duality, includingthe definition of duality, weak convergence and so on.In the third chapter, we study monotone duality. We define monotone dualityand discuss a theorem on the relationship between the extinct time and transientproblem.In the fourth chapter, we study moment duality. We define moment dualityand discuss its application.In the fifth chapter, we study Laplace duality. We define Laplace duality anddiscuss its application.