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Abstract: Application of Geometric Bounds to Convergence Rate of Markov Chains and Markov Processes on Ph.D. 2001 Wai Kong Yuen Department of Mathematics University of Toronto Quantitative geometric rates of convergence for reversible Markov chains are closely related to the spectral gap of the corresponding operator, which is hard to calculate for general state spaces. This thesis describes a geometric argument to give di erent types of bounds for spectral gaps of Markov chains on bounded... (Update)
Context of citations to this paper: More
...used a similar geometric arguments with paths to bound the second largest eigenvalue of a self adjoint discrete time Markov chain. Yuen [39] generalized the path argument to bound the spectral gap of a discrete time Markov chain on R n : In this paper, by considering some...
...Chapter 5 and discuss some possible development and improvement in the future. Parts of Chapters 1, 2 and 3 were already published in Yuen [44]. 1.2 Basic Notations and the Cheeger s Inequality In this section, we describe the type of Markov chains and Markov processes...
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BibTeX entry: (Update)
W.K. Yuen, Applications of geometric bounds to the convergence rate of Markov chains on R n , Stochastic processes and their Applications 87 (2000) 1-23. 37 http://citeseer.ist.psu.edu/yuen01application.html More
@misc{ yuen00applications,
author = "W. Yuen",
title = "Applications of geometric bounds to the convergence rate of Markov chains
on R n",
text = "W.K. Yuen, Applications of geometric bounds to the convergence rate of
Markov chains on R n , Stochastic processes and their Applications 87 (2000)
1-23. 37",
year = "2000",
url = "citeseer.ist.psu.edu/yuen01application.html" }
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82 A course in functional analysis (context) - Conway - 1985
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57 Introductory functional analysis with applications (context) - Kreyszig - 1978
51 Institute of Mathematical Statistics (context) - Diaconis, in et al. - 1988
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28 Geometric ergodicity and hybrid Markov chains - Roberts, Rosenthal - 1997
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4 Methods of mathematical physics IV (context) - Reed, Simon - 1978
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