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[ 洋図書 ] Compound renewal processes / ( Encyclopedia of mathematics and its applications ; 184 )

A.A. Borovkov ; translated by Alexey Alimov. -- Cambridge University Press, -- 2022, --

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ISBN 1009098446 (hardcover)
ISBN13桁 9781009098441 (hardcover)
無効なISBN等 9781009093965 (electronic publication)
テキストの言語 英語                  
原文の言語 ロシア語    
分類：NDC10版 410.8
個人著者標目 Borovkov, A. A.
姓名の完全形 (Aleksandr Alekseevich),
生没年等 1931-
本タイトル Compound renewal processes /
著者名 A.A. Borovkov ; translated by Alexey Alimov.
出版地・頒布地 Cambridge, United Kingdom ;
出版者・頒布者名 Cambridge University Press,
出版年・頒布年 2022,
数量 xvi, 362 pages :
他の形態的事項 illustrations ;
大きさ 25 cm.
書誌注記 Includes bibliographical references and index.
内容注記 Main limit laws in the normal deviation zone -- Integro-local limit theorems in the normal deviation zone -- Large deviation principles for compound renewal processes -- Large deviation principles for trajectories of compound renewal processes -- Integro-local limit theorems under the Cramér moment condition -- Exact asymptotics in boundary crossing problems for compound renewal processes -- Extension of the invariance principle to the zones of moderately large and small deviations -- Appendix. On boundary crossing problems for compound renewal processes when the Cramér condition is not fulfilled.
要約、抄録、注釈等 "Compound renewal processes (CRPs) are among the most ubiquitous models arising in applications of probability. At the same time, they are a natural generalization of random walks, the most well-studied classical objects in probability theory. This monograph, written for researchers and graduate students, presents the general asymptotic theory and generalizes many well-known results concerning random walks. The book contains the key limit theorems for CRPs, functional limit theorems, integro-local limit theorems, large and moderately large deviation principles for CRPs in the state space and in the space of trajectories, including large deviation principles in boundary crossing problems for CRPs, with an explicit form of the rate functionals, and an extension of the invariance principle for CRPs to the domain of moderately large and small deviations. Applications establish the key limit laws for Markov additive processes, including limit theorems in the domains of normal and large deviations"-- Provided by publisher.
著者標目 Alimov, Alexey.
統一タイトル(シリーズ副出標目) Encyclopedia of mathematics and its applications.
シリーズ名・巻次 Encyclopedia of mathematics and its applications ; 184
一般件名 Limit theorems (Probability theory)
Deviation (Mathematics)
資料情報1 『Compound renewal processes /』（Encyclopedia of mathematics and its applications ; 184）　A.A. Borovkov ; translated by Alexey Alimov.　Cambridge University Press,　2022, （所蔵館：中央　 請求記号：F/410.8/E56/E1-184　 資料コード：7115742421）
URL https://catalog.library.metro.tokyo.lg.jp/winj/opac/switch-detail.do?lang=ja&bibid=1352057082

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