Author : Kiyosi Itô
Release : 2015-12-24
Genre : Mathematics
Kind : eBook
Book Rating : 72X/5 ( reviews)

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Book Synopsis Poisson Point Processes and Their Application to Markov Processes by : Kiyosi Itô

Download or read book Poisson Point Processes and Their Application to Markov Processes written by Kiyosi Itô. This book was released on 2015-12-24. Available in PDF, EPUB and Kindle. Book excerpt: 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