Poisson Point Processes and Their Application to Markov Processes

ISBN-13: 9789811002717 / Angielski / Miękka / 2016 / 43 str.

Kiyosi Ito; Shinzo Watanabe; Ichiro Shigekawa

Opis

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. Ito, and H. P. McKean, among others. In this book, Ito 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 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 (called the jumping-in measure and a non-negative number m

Recenzje

"The main idea of this volume has had a profound influence on the boundary theory of Markov processes. This volume is beautifully written and it is a pleasure to read." (Ren Ming Song, Mathematical Reviews, December, 2016)

Spis treści

1. Poisson point processes.- 2. Application to Markov Process.