Limit theorems for random walks

被引：9

作者：

Bendikov, Alexander ^{[1
]}

Cygan, Wojciech ^{[1
]}

Trojan, Bartosz ^{[2
]}

机构：

[1] Uniwersytet Wroclawski, Inst Matemat, Pl Grunwaldzki 2-4, PL-50384 Wroclaw, Poland

[2] Wroclaw Univ Technol, Wydzial Matemat, Wyb Wyspianskiego 27, PL-50370 Wroclaw, Poland

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2017年 / 127卷 / 10期

基金：

奥地利科学基金会;

关键词：

Asymptotic formula; Random walk; Regular variation; Subordination; Strong ratio limit theorem; Functional limit theorem;

D O I：

10.1016/j.spa.2017.02.008

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider a random walk S-tau which is obtained from the simple random walk S by a discrete time version of Bochner's subordination. We prove that under certain conditions on the subordinator tau appropriately scaled random walk S-tau converges in the Skorohod space to the symmetric alpha-stable process B-alpha We also prove asymptotic formula for the transition function of S-tau similar to the Polya's asymptotic formula for B-alpha. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：3268 / 3290

页数：23

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