Poisson Point Processes and Their Application to Markov Processes (SpringerBriefs in Probability and Mathematical Statistics)
Itô, Kiyosi
ISBN 10: 9811002711 ISBN 13: 9789811002717
Edité par Springer, 2015
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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
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Titre : Poisson Point Processes and Their ...
Éditeur : Springer
Date d'édition : 2015
Reliure : Paperback
Etat : Like New
Type de livre : book
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Poisson Point Processes and Their Application to Markov Processes
Edité par
Springer, 2016
ISBN 10 : 9811002711
ISBN 13 : 9789811002717
Ancien ou d'occasion
Couverture souple
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Poisson Point Processes and Their Application to Markov Processes
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Springer Nature Singapore, Springer Nature Singapore Feb 2016, 2016
ISBN 10 : 9811002711
ISBN 13 : 9789811002717
Neuf
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Taschenbuch. Etat : Neu. Neuware -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 ¿ Scalled 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) onS{a}(called the jumping-in measure and a non-negative number mSpringer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 56 pp. Englisch. N° de réf. du vendeur 9789811002717
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Poisson Point Processes and Their Application to Markov Processes
Edité par
Springer Nature Singapore Feb 2016, 2016
ISBN 10 : 9811002711
ISBN 13 : 9789811002717
Neuf
Taschenbuch
Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
Évaluation du vendeur 5 sur 5 étoiles
Taschenbuch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 56 pp. Englisch. N° de réf. du vendeur 9789811002717
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Poisson Point Processes and Their Application to Markov Processes (Paperback)
Edité par
Springer Verlag, Singapore, Singapore, 2016
ISBN 10 : 9811002711
ISBN 13 : 9789811002717
Neuf
Paperback
Edition originale
Vendeur : Grand Eagle Retail, Bensenville, IL, Etats-Unis
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Paperback. Etat : new. Paperback. 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. 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. For this, Ito used, as a fundamental tool, the notion of Poisson point processes formed of all excursions of the process on S \ {a}. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. N° de réf. du vendeur 9789811002717
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