Poisson Point Processes and Their Application to Markov Processes
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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. It?, and H. P. McKean, among others. In this book, It? 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
Format:Paperback
Language:English
ISBN:9811002711
ISBN13:9789811002717
Release Date:February 2016
Publisher:Springer
Length:43 Pages
Weight:0.20 lbs.
Dimensions:0.1" x 6.1" x 9.2"
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