Electronic Journal of Probability

Exponential Approximation for the Nearly Critical Galton-Watson Process and Occupation Times of Markov Chains

Erol Peköz and Adrian Röllin

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Abstract

In this article we provide new applications for exponential approximation using the framework of Peköz and Röllin (2011), which is based on Stein's method. We give error bounds for the nearly critical Galton-Watson process conditioned on non-extinction, and for the occupation times of Markov chains; for the latter, in particular, we give a new exponential approximation rate for the number of revisits to the origin for general two dimensional random walk, also known as the Erdös-Taylor theorem.

Article information

Source
Electron. J. Probab., Volume 16 (2011), paper no. 51, 1381-1393.

Dates
Accepted: 10 August 2011
First available in Project Euclid: 1 June 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1464820220

Digital Object Identifier
doi:10.1214/EJP.v16-914

Mathematical Reviews number (MathSciNet)
MR2827464

Zentralblatt MATH identifier
1245.60083

Subjects
Primary: 60F05: Central limit and other weak theorems
Secondary: 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
Exponential distribution Stein's method nearly critical Galton-Watson branching process occupation times of Markov chains ErdH{o}s-Taylor theorem

Rights
This work is licensed under aCreative Commons Attribution 3.0 License.

Citation

Peköz, Erol; Röllin, Adrian. Exponential Approximation for the Nearly Critical Galton-Watson Process and Occupation Times of Markov Chains. Electron. J. Probab. 16 (2011), paper no. 51, 1381--1393. doi:10.1214/EJP.v16-914. https://projecteuclid.org/euclid.ejp/1464820220


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