Verfügbarkeit: Poisson point processes and their application to Markov processes

Poisson point processes and their application to Markov processes:

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Bibliographische Detailangaben
1. Verfasser:	Itō, Kiyoshi 1915-2008 (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Singapore Springer [2015]
Schriftenreihe:	SpringerBriefs in probability and mathematical statistics
Schlagworte:	Mathematics Functional analysis Measure theory Probabilities Probability Theory and Stochastic Processes Measure and Integration Functional Analysis Mathematik
Online-Zugang:	BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Abstract
Beschreibung:	1 Online Ressource (XI, 43 Seiten, 3 illus. in color)
ISBN:	9789811002724
ISSN:	2365-4333
DOI:	10.1007/978-981-10-0272-4

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MARC


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Datensatz im Suchindex

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adam_text	POISSON POINT PROCESSES AND THEIR APPLICATION TO MARKOV PROCESSES / ITO, KIYOSI : 2015 ABSTRACT / INHALTSTEXT 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 DIESES SCHRIFTSTUECK WURDE MASCHINELL ERZEUGT.
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author	Itō, Kiyoshi 1915-2008
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isbn	9789811002724
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spelling	Itō, Kiyoshi 1915-2008 Verfasser (DE-588)119388073 aut Poisson point processes and their application to Markov processes Kiyosi Itô Singapore Springer [2015] © 2015 1 Online Ressource (XI, 43 Seiten, 3 illus. in color) txt rdacontent c rdamedia cr rdacarrier SpringerBriefs in probability and mathematical statistics 2365-4333 Mathematics Functional analysis Measure theory Probabilities Probability Theory and Stochastic Processes Measure and Integration Functional Analysis Mathematik Erscheint auch als Druckausgabe 978-981-10-0271-7 https://doi.org/10.1007/978-981-10-0272-4 Verlag Volltext Springer Fremddatenuebernahme application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730274&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Abstract
spellingShingle	Itō, Kiyoshi 1915-2008 Poisson point processes and their application to Markov processes Mathematics Functional analysis Measure theory Probabilities Probability Theory and Stochastic Processes Measure and Integration Functional Analysis Mathematik
title	Poisson point processes and their application to Markov processes
title_auth	Poisson point processes and their application to Markov processes
title_exact_search	Poisson point processes and their application to Markov processes
title_full	Poisson point processes and their application to Markov processes Kiyosi Itô
title_fullStr	Poisson point processes and their application to Markov processes Kiyosi Itô
title_full_unstemmed	Poisson point processes and their application to Markov processes Kiyosi Itô
title_short	Poisson point processes and their application to Markov processes
title_sort	poisson point processes and their application to markov processes
topic	Mathematics Functional analysis Measure theory Probabilities Probability Theory and Stochastic Processes Measure and Integration Functional Analysis Mathematik
topic_facet	Mathematics Functional analysis Measure theory Probabilities Probability Theory and Stochastic Processes Measure and Integration Functional Analysis Mathematik
url	https://doi.org/10.1007/978-981-10-0272-4 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=028730274&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT itokiyoshi poissonpointprocessesandtheirapplicationtomarkovprocesses

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