Weak convergence of random walks, conditioned to stay away from small sets-Reference-Cited by-同舟云学术

Weak convergence of random walks, conditioned to stay away from small sets

Published:2013-03-01 Issue:1 Volume:50 Page:122-128
ISSN:0081-6906
Container-title:Studia Scientiarum Mathematicarum Hungarica
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Author:

Pajor-Gyulai Zsolt¹,Szász Domokos²

Affiliation:

1. 1 University of Maryland Department of Mathematics, Mathematics Building College Park MD 20742-4015 USA

2. 2 Budapest University of Technology and Economics Department of Stochastics, Institute of Mathematics 1111 Egry J. u. 1 Budapest Hungary

Abstract

Let {Xn}n∈ℕ be a sequence of i.i.d. random variables in ℤd. Let Sk = X1 + … + Xk and Yn(t) be the continuous process on [0, 1] for which Yn(k/n) = Sk/n1/2 for k = 1, … n and which is linearly interpolated elsewhere. The paper gives a generalization of results of ([2]) on the weak limit laws of Yn(t) conditioned to stay away from some small sets. In particular, it is shown that the diffusive limit of the random walk meander on ℤd: d ≧ 2 is the Brownian motion.

Publisher

Akademiai Kiado Zrt.

Subject

General Mathematics

Link

https://www.akademiai.com/doi/pdf/10.1556/sscmath.50.2013.1.1232

Reference8 articles.

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