Algebraic convergence of Markov chains
نویسندگان
چکیده
منابع مشابه
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...
متن کاملConvergence 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...
متن کاملAlgebraic Multigrid for Markov Chains
An algebraic multigrid (AMG) method is presented for the calculation of the stationary probability vector of an irreducible Markov chain. The method is based on standard AMG for nonsingular linear systems, but in a multiplicative, adaptive setting. A modified AMG interpolation formula is proposed that produces a nonnegative interpolation operator with unit row sums. We show how the adoption of ...
متن کاملConvergence Rates for Markov Chains
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متن کاملConvergence for periodic Markov chains
Consider a discrete-time Markov chain (Xn : n > 0) ∼ Markov(λ, P ) with countable state space S. In the last lecture, we proved the following theorem for aperiodic Markov chains. Theorem (Aperiodic case). Assume P is irreducible and positive recurrent with unique invariant measure π. If, in addition, P is aperiodic, then P(Xn = j)→ πj as n→∞ for all j ∈ S. In particular, p (n) ij → πj as n→∞ fo...
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ژورنال
عنوان ژورنال: The Annals of Applied Probability
سال: 2003
ISSN: 1050-5164
DOI: 10.1214/aoap/1050689596