The Annals of Applied Probability

$L^2$ Convergence of Time Nonhomogeneous Markov Processes: I. Spectral Estimates

Jean-Dominique Deuschel and Christian Mazza

Full-text: Open access

Abstract

We study the convergence of nonsymmetric annealing processes, extending the classical Dirichlet form approach to a broad class of Markov chains with exponentially vanishing transition functions. We show that both the true and symmetrized spectral gaps are logarithmically equivalent, and give robust estimates for the gap using geometric methods.

Article information

Source
Ann. Appl. Probab., Volume 4, Number 4 (1994), 1012-1056.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aoap/1177004901

Digital Object Identifier
doi:10.1214/aoap/1177004901

Mathematical Reviews number (MathSciNet)
MR1304771

Zentralblatt MATH identifier
0819.60063

JSTOR
links.jstor.org

Subjects
Primary: 60J27: Continuous-time Markov processes on discrete state spaces
Secondary: 60F10: Large deviations 93E25: Other computational methods 15A18: Eigenvalues, singular values, and eigenvectors 60J60: Diffusion processes [See also 58J65]

Keywords
Dirichlet forms first hitting time geometric bounds $L^2$ convergence Metropolis nonsymmetric Markov chains spectral gap ultrametricity

Citation

Deuschel, Jean-Dominique; Mazza, Christian. $L^2$ Convergence of Time Nonhomogeneous Markov Processes: I. Spectral Estimates. Ann. Appl. Probab. 4 (1994), no. 4, 1012--1056. doi:10.1214/aoap/1177004901. https://projecteuclid.org/euclid.aoap/1177004901


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