Poisson point processes and their application to Markov processes:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore
Springer
[2015]
|
| Series: | SpringerBriefs in probability and mathematical statistics
|
| Subjects: | |
| Online Access: | BTU01 FRO01 TUM01 UBM01 UBT01 UBW01 UPA01 Volltext Abstract |
| Physical Description: | 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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Record in the Search Index
| _version_ | 1804175846577012736 |
|---|---|
| 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.
|
| any_adam_object | 1 |
| author | Itō, Kiyoshi 1915-2008 |
| author_GND | (DE-588)119388073 |
| author_facet | Itō, Kiyoshi 1915-2008 |
| author_role | aut |
| author_sort | Itō, Kiyoshi 1915-2008 |
| author_variant | k i ki |
| building | Verbundindex |
| bvnumber | BV043309585 |
| classification_tum | MAT 000 |
| collection | ZDB-2-SMA |
| ctrlnum | (OCoLC)934210682 (DE-599)BVBBV043309585 |
| dewey-full | 519.2 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 519 - Probabilities and applied mathematics |
| dewey-raw | 519.2 |
| dewey-search | 519.2 |
| dewey-sort | 3519.2 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-981-10-0272-4 |
| format | Electronic eBook |
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| id | DE-604.BV043309585 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T07:22:47Z |
| institution | BVB |
| isbn | 9789811002724 |
| issn | 2365-4333 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-028730274 |
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| physical | 1 Online Ressource (XI, 43 Seiten, 3 illus. in color) |
| psigel | ZDB-2-SMA UBY_PDA_SMA ZDB-2-SMA_2015 |
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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 |
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