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Functional Limit Theorems for Compound Renewal Processes Научная публикация

Журнал

Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260

Вых. Данные

Год: 2019, Том: 60, Номер: 1, Страницы: 27-40 Страниц : 14 DOI: 10.1134/S003744661901004X

Ключевые слова

Anscombe’s theorem; compound renewal processes; convergence to a stable process; functional limit theorems; invariance principle

Авторы

Borovkov A.A. ^1,2

Организации

1	Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russian Federation
2	Novosibirsk State University

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.

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

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

Web of science:	WOS:000464720000004
Scopus:	2-s2.0-85065244952
OpenAlex:	W2936414956

БД	Цитирований
Scopus	2
OpenAlex	3
Web of science	2