On convergence of homogeneous Markov chains

Convergence of symmetric Markov chains on Z

For each n let Y (n) t be a continuous time symmetric Markov chain with state space n −1 Z d. Conditions in terms of the conductances are given for the convergence of the Y (n) t to a symmetric Markov process Yt on R d. We have weak convergence of {Y (n) t : t ≤ t0} for every t0 and every starting point. The limit process Y has a continuous part and may also have jumps.

Continuous-time homogeneous Markov chains

Convergence Rates of Markov Chains

This is an expository paper which presents various ideas related to nonasymptotic rates of convergence for Markov chains. Such rates are of great importance for stochastic algorithms which are widely used in statistics and in computer science. They also have applications to analysis of card shuffling and other areas. In this paper, we attempt to describe various mathematical techniques which ha...

Convergence Rates of Markov Chains

1. Orientation 1 1.1. Example 1: Random-to-Top Card Shuffling 1 1.2. Example 2: The Ehrenfest Urn Model of Diffusion 2 1.3. Example 3: Metropolis-Hastings Algorithm 4 1.4. Reversible Markov Chains 5 1.5. Exercises: Reversiblity, Symmetries and Stationary Distributions 8 2. Coupling 9 2.1. Coupling and Total Variation Distance 9 2.2. Coupling Constructions and Convergence of Markov Chains 10 2.3...

Convergence Rates for Markov Chains

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