POISSON POINT PROCESSES AND THEIR APPLICATION TO MARKOV PROCESSES by Kiyosi Ito, Shinzo Watanabe (Foreword), Ichiro Shigekawa (Foreword) ( 9789811002717 )

Item Details

Title:

POISSON POINT PROCESSES AND THEIR APPLICATION TO MARKOV PROCESSES

Volume:

2015

By:

Kiyosi Ito, Shinzo Watanabe (Foreword), Ichiro Shigekawa (Foreword)

Format:

Paperback

List price:	£37.99
We currently do not stock this item, please contact the publisher directly for further information.

ISBN 10:

9811002711

ISBN 13:

9789811002717

Publisher:

SPRINGER VERLAG, SINGAPORE

Pub. date:

24 December, 2015

Edition:

2015 ed.

Series:

SpringerBriefs in Probability and Mathematical Statistics 1

Pages:

Synopsis:

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 \ {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, Ito used, as a fundamental tool, the notion of Poisson point processes formed of all excursions of the process on S \ {a}.This theory of Ito'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 Ito 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 Ito's beautiful and impressive lectures in his day.

Illustrations:

3 black & white illustrations, biography

Publication:

Singapore

Imprint:

Springer Verlag, Singapore

Returns:

Returnable

Some other items by this author:

AN INTRODUCTION TO PROBABILITY THEORY (PB)

COLLECTED PAPERS (HB)

COLLECTED PAPERS (PB)