Exponential approximation for the nearly critical Galton-Watson process and occupation times of Markov chains

Details Exponential approximation for the nearly critical Galton-Watson process and occupation times of Markov chains Exponential approximation for the nearly critical Galton-Watson process and occupation times of Markov chains

2010-08-24

arxiv.org/abs/1008.3947v1

Mathematics

Probability

14 pages

Scientific paper

In this article we provide new applications for exponential approximation using the framework of Pek\"oz and R\"ollin (in press), 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 Erd\H{o}s-Taylor theorem.

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