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Compound renewal processes

Borovkov, A. A.

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Compound renewal processes

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Compound renewal processes/ A. A. Borovkov ; translated by Alexey Alimov.
作者:	Borovkov, A. A.
其他作者:	Alimov, Alexey,
出版者:	Cambridge ; New York :Cambridge University Press, : 2022.,
面頁冊數:	xvi, 362 p. :ill., digital ;24 cm.
附註:	Title from publisher's bibliographic system (viewed on 20 Jun 2022).
內容註:	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.
標題:	Limit theorems (Probability theory) -
電子資源:	https://doi.org/10.1017/9781009093965
ISBN:	9781009093965

Compound renewal processes
Borovkov, A. A.

Compound renewal processes[electronic resource] /A. A. Borovkov ; translated by Alexey Alimov. - Cambridge ; New York :Cambridge University Press,2022. - xvi, 362 p. :ill., digital ;24 cm. - Encyclopedia of mathematics and its applications ;184. - 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.

ISBN: 9781009093965Subjects--Topical Terms:

646262
Limit theorems (Probability theory)

LC Class. No.: QA273.67 / .B67 2022

Dewey Class. No.: 519.2

Compound renewal processes
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500 $a Title from publisher's bibliographic system (viewed on 20 Jun 2022).
500 $a Translated from the Russian.
505 0 $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.
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