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Bücher Wissen & Bildung Englische Bücher Naturwissenschaft, Medizin, Informatik, Technik Mathematik Wahrscheinlichkeitstheorie & Statistik Poisson Point Processes and Their Application to Markov Processes
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Poisson Point Processes and Their Application to Markov Processes
Kiyosi Itô (Broschiert, Englisch)
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Beschreibung
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. Dieses Produkt haben wir gerade leider nicht auf Lager.
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Technische Daten
Erscheinungsdatum
01.02.2016
Sprache
Englisch
EAN
9789811002717
Herausgeber
Springer Singapore
Serien- oder Bandtitel
SpringerBriefs in Probability and Mathematical Statistics
Sonderedition
Nein
Autor
Kiyosi Itô
Seitenanzahl
43
Einbandart
Broschiert
Schlagwörter
Poisson point process, Poisson point process of excursions, characteristic measure, jumping-in measure and stagnancy rate, discontinuous and continuous entrance points
Thema-Inhalt
PBT - Wahrscheinlichkeitsrechnung und Statistik
PBWL - Stochastik
PBKL - Integralrechnung und -gleichungen
PBKF - Funktionalanalysis und Abwandlungen
Höhe
235 mm
Breite
15.5 cm
Hersteller: Springer Nature Customer Service Center GmbH, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com
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