Poisson Point Processes and Their Application to Markov Processes

An extension problem (often called a boundary problem) of Markov processes has been studied, particularly in the case of one-dimensional diffusion processes, by W. Feller, K. Itô, and H. P. McKean, among others. In this book, Itô discussed a case of a general Markov process with state space S and a specified point a ? S called a boundary. The problem is to obtain all possible recurrent extensions of a given minimal process (i.e., the process on S \ {a} which is absorbed on reaching the boundary a). The study in this lecture is restricted to a simpler case of the boundary a being a discontinuous entrance point, leaving a more general case of a continuous entrance point to future works. He established a one-to-one correspondence between a recurrent extension and a pair of a positive measure k(db) on S \ {a} (called the jumping-in measure and a non-negative number m

• | Author: Kiyosi Itô
• | Publisher: Springer
• | Publication Date: Feb 01, 2016
• | Number of Pages: NA pages
• | Language: English
• | Binding: Paperback
• | ISBN-10: 9811002711
• | ISBN-13: 9789811002717