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The Resource Poisson point processes and their application to Markov processes, Kiyosi Itô ; foreword by Shinzo Watanabe and Ichiro Shigekawa, (electronic book)

Poisson point processes and their application to Markov processes, Kiyosi Itô ; foreword by Shinzo Watanabe and Ichiro Shigekawa, (electronic book)

Label
Poisson point processes and their application to Markov processes
Title
Poisson point processes and their application to Markov processes
Statement of responsibility
Kiyosi Itô ; foreword by Shinzo Watanabe and Ichiro Shigekawa
Creator
Author
Subject
Language
eng
Summary
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 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 Itô 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 Itô's beautiful and impressive lectures in his day
Member of
Cataloging source
GW5XE
http://library.link/vocab/creatorDate
1915-2008
http://library.link/vocab/creatorName
Itō, Kiyosi
Dewey number
519.2/4
Illustrations
illustrations
Index
no index present
LC call number
QA274.42
Literary form
non fiction
Nature of contents
  • dictionaries
  • bibliography
Series statement
SpringerBriefs in probability and mathematical statistics,
http://library.link/vocab/subjectName
  • Poisson processes
  • Markov processes
Label
Poisson point processes and their application to Markov processes, Kiyosi Itô ; foreword by Shinzo Watanabe and Ichiro Shigekawa, (electronic book)
Instantiates
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Control code
SPR933761010
Dimensions
unknown
Extent
1 online resource (xi, 43 pages)
File format
unknown
Form of item
online
Isbn
9789811002717
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-981-10-0272-4
Other physical details
color illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Reproduction note
Electronic resource.
Sound
unknown sound
Specific material designation
remote
Label
Poisson point processes and their application to Markov processes, Kiyosi Itô ; foreword by Shinzo Watanabe and Ichiro Shigekawa, (electronic book)
Publication
Antecedent source
unknown
Bibliography note
Includes bibliographical references
Carrier category
online resource
Carrier category code
  • cr
Carrier MARC source
rdacarrier
Color
multicolored
Content category
text
Content type code
  • txt
Content type MARC source
rdacontent
Control code
SPR933761010
Dimensions
unknown
Extent
1 online resource (xi, 43 pages)
File format
unknown
Form of item
online
Isbn
9789811002717
Level of compression
unknown
Media category
computer
Media MARC source
rdamedia
Media type code
  • c
Other control number
10.1007/978-981-10-0272-4
Other physical details
color illustrations.
Quality assurance targets
not applicable
Reformatting quality
unknown
Reproduction note
Electronic resource.
Sound
unknown sound
Specific material designation
remote

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