| 书目名称 | Poisson Point Processes and Their Application to Markov Processes | | 编辑 | Kiyosi Itô | | 视频video | | | 概述 | Gives a beautiful elementary treatment of general Poisson point processes in Chapter 1, especially recommended for beginners.Shows how the notion of Poisson point processes with values in a function s | | 丛书名称 | SpringerBriefs in Probability and Mathematical Statistics | | 图书封面 |  | | 描述 | 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< (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, Itô used, as a fundamental tool, the notion of Poisson point processes formed of all excursions of the process on S {a}. This theory of Itô‘s of Poisson point proc | | 出版日期 | Book 2015 | | 关键词 | Poisson point process; Poisson point process of excursions; characteristic measure; jumping-in measure | | 版次 | 1 | | doi | https://doi.org/10.1007/978-981-10-0272-4 | | isbn_softcover | 978-981-10-0271-7 | | isbn_ebook | 978-981-10-0272-4Series ISSN 2365-4333 Series E-ISSN 2365-4341 | | issn_series | 2365-4333 | | copyright | The Author(s) 2015 |
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发表于 2025-3-21 18:26:28
