Poisson Point Processes and Their Application to Markov Processes (SpringerBriefs in Probability and Mathematical Statistics)

Kiyosi It�, Shinzo Watanabe, Ichiro Shigekawa

ISBN 10: 9811002711 / ISBN 13: 9789811002717

Edité par Springer 2016-01-25, 2016

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N° de réf. du vendeur 6666-IUK-9789811002717

Détails bibliographiques

• Titre: Poisson Point Processes and Their Application to Markov Processes (SpringerBriefs in Probability and Mathematical Statistics)
• Éditeur: Springer 2016-01-25
• Date de parution: 2016
• Langue: anglais
• ISBN à 10 chiffres: 9811002711
• ISBN à 13 chiffres: 9789811002717
• Reliure: Paperback
• État de l'article: New

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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. 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