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Stein's Method for Compound Geometric Approximation

Part of: Distribution theory Distribution theory - Probability Markov processes

Published online by Cambridge University Press:  14 July 2016

Fraser Daly
Fraser Daly*
Affiliation:
Universität Zürich
*
∗ Postal address: Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, CH-8057 Zürich, Switzerland. Email address: fraser.daly@math.uzh.ch
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Abstract

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We apply Stein's method for probabilistic approximation by a compound geometric distribution, with applications to Markov chain hitting times and sequence patterns. Bounds on our Stein operator are found using a complex analytical approach based on generating functions and Cauchy's formula.

Keywords

Stein's methodcompound geometric approximationMarkov chain hitting times

MSC classification

Secondary: 62E17: Approximations to distributions (nonasymptotic) 60E15: Inequalities; stochastic orderings 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Information

Type
Research Article
Information
Journal of Applied Probability , Volume 47 , Issue 1 , March 2010 , pp. 146 - 156
Copyright
Copyright © Applied Probability Trust 2010 

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