Functional Limit Theorems for Compound Renewal Processes Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2019, Volume: 60, Number: 1, Pages: 27-40 Pages count : 14 DOI: 10.1134/S003744661901004X | ||||
| Tags | Anscombe’s theorem; compound renewal processes; convergence to a stable process; functional limit theorems; invariance principle | ||||
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Abstract:
We generalize Anscombe’s Theorem to the case of stochastic processes converging to a continuous random process. As applications, we find a simple proof of an invariance principle for compound renewal processes (CRPs) in the case of finite variance of the elements of the control sequence. We find conditions, close to minimal ones, of the weak convergence of CRPs in the metric space D with metrics of two types to stable processes in the case of infinite variance. They turn out narrower than the conditions for convergence of a distribution in this space. © 2019, Pleiades Publishing, Ltd.
Cite:
Borovkov A.A.
Functional Limit Theorems for Compound Renewal Processes
Siberian Mathematical Journal. 2019. V.60. N1. P.27-40. DOI: 10.1134/S003744661901004X WOS Scopus OpenAlex
Functional Limit Theorems for Compound Renewal Processes
Siberian Mathematical Journal. 2019. V.60. N1. P.27-40. DOI: 10.1134/S003744661901004X WOS Scopus OpenAlex
Original:
Боровков А.А.
Функциональные предельные теоремы для обобщенных процессов восстановления
Сибирский математический журнал. 2019. Т.60. №1. С.37–54. DOI: 10.33048/smzh.2019.60.104 РИНЦ OpenAlex
Функциональные предельные теоремы для обобщенных процессов восстановления
Сибирский математический журнал. 2019. Т.60. №1. С.37–54. DOI: 10.33048/smzh.2019.60.104 РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000464720000004 |
| Scopus: | 2-s2.0-85065244952 |
| OpenAlex: | W2936414956 |