Functional Limit Theorems for Compound Renewal Processes

Сибирский математический журнал

A. A. Borovkov¹ 

[1] Novosibirsk State University

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

DOI  :  10.1134/S003744661901004X

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

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.

【 授权许可】

CC BY