Transient Nearest Neighbor Random Walk and Bessel Process

被引：0

作者：

Endre Csáki

Antónia Földes

Pál Révész

机构：

[1] Hungarian Academy of Sciences,Alfréd Rényi Institute of Mathematics

[2] College of Staten Island,Department of Mathematics

[3] CUNY,Institut für Statistik und Wahrscheinlichkeitstheorie

[4] Technische Universität Wien,undefined

来源：

Journal of Theoretical Probability | 2009年 / 22卷

关键词：

Transient random walk; Bessel process; Strong invariance principle; Local time; Strong theorems; 60F17; 60F15; 60J10; 60J55; 60J60;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

We prove a strong invariance principle between a transient Bessel process and a certain nearest neighbor (NN) random walk that is constructed from the former by using stopping times. We show that their local times are close enough to share the same strong limit theorems. It is also shown that if the difference between the distributions of two NN random walks are small, then the walks themselves can be constructed in such a way that they are close enough. Finally, some consequences concerning strong limit theorems are discussed.

引用

页码：992 / 1009

页数：17

共 19 条

[1]

Adelman O.(1996)The measure of the overlap of past and future under a transient Bessel process Stoch. Stoch. Rep. 57 169-183

[2]

Shi Z.(1971)An extension of Khintchine’s estimate for large deviations to a class of Markov chains converging to a singular diffusion Commun. Pure Appl. Math. 24 705-726

[3]

Brézis H.(2006)The lower envelope of positive self-similar Markov processes Electron. J. Probab. 11 1321-1341

[4]

Rosenkrantz W.(1998)Analysis of random walks using orthogonal polynomials J. Comput. Appl. Math. 99 387-399

[5]

Singer B.(2001)First return probabilities of birth and death chains and associated orthogonal polynomials Proc. Am. Math. Soc. 129 1805-1815

[6]

Chaumont L.(1959)Random walks Ill. J. Math. 3 66-81

[7]

Pardo J.C.(1996)On a problem of Erdős and Taylor Ann. Probab. 24 761-787

[8]

Coolen-Schrijner P.(1962)A new class of probability limit theorems J. Math. Mech. 11 749-772

[9]

Van Doorn E.A.(1973)Sample functions of the Ann. Probab. 1 138-163

[10]

Dette H.(1995)-parameter Wiener process Stoch. Process. Appl. 60 87-102

← 1 2 →