Bootstrap random walks

被引：5

作者：

Collevecchio, Andrea ^{[1
]}

Hamza, Kais ^{[1
]}

Shi, Meng ^{[1
]}

机构：

[1] Monash Univ, Sch Math Sci, Clayton, Vic 3800, Australia

来源：

STOCHASTIC PROCESSES AND THEIR APPLICATIONS | 2016年 / 126卷 / 06期

基金：

澳大利亚研究理事会;

关键词：

Random walks; Functional limit theorem;

D O I：

10.1016/j.spa.2015.11.016

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：

Consider a one dimensional simple random walk X = (X-n)(n >= 0). We form a new simple symmetric random walk Y = (Y-n)(n >= 0) by taking sums of products of the increments of X and study the two-dimensional walk (X, Y) = ((X-n, Y-n))(n >= 0). We show that it is recurrent and when suitably normalised converges to a two-dimensional Brownian motion with independent components; this independence occurs despite the functional dependence between the pre-limit processes. The process of recycling increments in this way is repeated and a multi -dimensional analog of this limit theorem together with a transience result are obtained. The construction and results are extended to include the case where the increments take values in a finite set (not necessarily {-1, +1}). (C) 2015 Elsevier B.V. All rights reserved.

引用

页码：1744 / 1760

页数：17