Compound renewal processes:
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 stud...
Gespeichert in:
| 1. Verfasser: | |
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| Weitere Verfasser: | |
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Cambridge ; New York
Cambridge University Press
2022
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| Ausgabe: | First published |
| Schriftenreihe: | Encyclopedia of mathematics and its applications
184 |
| Schlagworte: | |
| Zusammenfassung: | 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 |
| Beschreibung: | Title from publisher's bibliographic system (viewed on 20 Jun 2022) 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 |
| Beschreibung: | xvi, 362 Seiten |
| ISBN: | 9781009098441 |
Internformat
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| 500 | |a 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 | ||
| 520 | |a 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 | ||
| 650 | 4 | |a Limit theorems (Probability theory) | |
| 650 | 4 | |a Deviation (Mathematics) | |
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| id | DE-604.BV048404436 |
| illustrated | Not Illustrated |
| index_date | 2024-07-03T20:23:40Z |
| indexdate | 2024-07-10T09:37:11Z |
| institution | BVB |
| isbn | 9781009098441 |
| language | English |
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| physical | xvi, 362 Seiten |
| publishDate | 2022 |
| publishDateSearch | 2022 |
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| publisher | Cambridge University Press |
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| series | Encyclopedia of mathematics and its applications |
| series2 | Encyclopedia of mathematics and its applications |
| spelling | Borovkov, A. A. 1931- (DE-588)1089930224 aut Compound renewal processes A.A. Borovkov: Sobolev Institute of Mathematics, Russia ; translated by Alexey Alimov: Steklov Institute of Mathematics, Moscow First published Cambridge ; New York Cambridge University Press 2022 xvi, 362 Seiten txt rdacontent n rdamedia nc rdacarrier Encyclopedia of mathematics and its applications 184 Title from publisher's bibliographic system (viewed on 20 Jun 2022) 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 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 Limit theorems (Probability theory) Deviation (Mathematics) Alimov, Aleksej R. 1971- (DE-588)1263132081 trl Erscheint auch als Online-Ausgabe 978-1-00-909396-5 Encyclopedia of mathematics and its applications 184 (DE-604)BV000903719 184 |
| spellingShingle | Borovkov, A. A. 1931- Compound renewal processes Encyclopedia of mathematics and its applications Limit theorems (Probability theory) Deviation (Mathematics) |
| title | Compound renewal processes |
| title_auth | Compound renewal processes |
| title_exact_search | Compound renewal processes |
| title_exact_search_txtP | Compound renewal processes |
| title_full | Compound renewal processes A.A. Borovkov: Sobolev Institute of Mathematics, Russia ; translated by Alexey Alimov: Steklov Institute of Mathematics, Moscow |
| title_fullStr | Compound renewal processes A.A. Borovkov: Sobolev Institute of Mathematics, Russia ; translated by Alexey Alimov: Steklov Institute of Mathematics, Moscow |
| title_full_unstemmed | Compound renewal processes A.A. Borovkov: Sobolev Institute of Mathematics, Russia ; translated by Alexey Alimov: Steklov Institute of Mathematics, Moscow |
| title_short | Compound renewal processes |
| title_sort | compound renewal processes |
| topic | Limit theorems (Probability theory) Deviation (Mathematics) |
| topic_facet | Limit theorems (Probability theory) Deviation (Mathematics) |
| volume_link | (DE-604)BV000903719 |
| work_keys_str_mv | AT borovkovaa compoundrenewalprocesses AT alimovaleksejr compoundrenewalprocesses |