(DOWNLOAD) "Poisson Point Processes and Their Application to Markov Processes" by Kiyosi It么 * eBook PDF Kindle ePub Free
eBook details
- Title: Poisson Point Processes and Their Application to Markov Processes
- Author : Kiyosi It么
- Release Date : January 24, 2015
- Genre: Mathematics,Books,Science & Nature,
- Pages : * pages
- Size : 1770 KB
Description
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么, and H. P. McKean, among others. In this book, It么 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< (called the stagnancy rate). The necessary and sufficient conditions for a pair k, m was obtained so that the correspondence is precisely described. For this, It么 used, as a fundamental tool, the notion of Poisson point processes formed of all excursions of the process on S \ {a}. This theory of It么's of Poisson point processes of excursions is indeed a breakthrough. It has been expanded and applied to more general extension problems by many succeeding researchers. Thus we may say that this lecture note by It么 is really a memorial work in the extension problems of Markov processes. Especially in Chapter 1 of this note, a general theory of Poisson point processes is given that reminds us of It么's beautiful and impressive lectures in his day.
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