scholarly journals Optimal Hoeffding bounds for discrete reversible Markov chains

2004 ◽  
Vol 14 (2) ◽  
pp. 958-970 ◽  
Author(s):  
Carlos A. León ◽  
François Perron
Keyword(s):  
Markov Chains ◽  
Reversible Markov Chains ◽  
Hoeffding Bounds

Geometric L 2 and L 1 convergence are equivalent for reversible Markov chains

2001 ◽  
Vol 38 (A) ◽  
pp. 37-41 ◽  
Author(s):  
Gareth O. Roberts ◽  
Richard L. Tweedie
Keyword(s):  
Markov Chains ◽  
Queueing Models ◽  
Gibbs Samplers ◽  
Reversible Markov Chains

The paper proves the statement of the title, and shows that it has useful applications in evaluating the convergence of queueing models and Gibbs samplers with deterministic and random scans.

On the invariance principle for reversible Markov chains

2016 ◽  
Vol 53 (2) ◽  
pp. 593-599 ◽  
Author(s):  
Magda Peligrad ◽  
Sergey Utev
Keyword(s):  
Standard Deviation ◽  
Central Limit Theorem ◽  
Limit Theorem ◽  
Markov Chains ◽  
Stochastic Processes ◽  
Partial Sums ◽  
Additive Functionals ◽  
Functional Clt ◽  
Reversible Markov Chains ◽  
Functional Central Limit

Abstract In this paper we investigate the functional central limit theorem (CLT) for stochastic processes associated to partial sums of additive functionals of reversible Markov chains with general spate space, under the normalization standard deviation of partial sums. For this case, we show that the functional CLT is equivalent to the fact that the variance of partial sums is regularly varying with exponent 1 and the partial sums satisfy the CLT. It is also equivalent to the conditional CLT.

On the Convergence of Reversible Markov Chains

1993 ◽  
Vol 14 (4) ◽  
pp. 950-966 ◽  
Author(s):  
Madhav P. Desai ◽  
Vasant B. Rao
Keyword(s):  
Markov Chains ◽  
Reversible Markov Chains

Geometric L2 and L1 convergence are equivalent for reversible Markov chains

2001 ◽  
Vol 38 (A) ◽  
pp. 37-41 ◽  
Author(s):  
Gareth O. Roberts ◽  
Richard L. Tweedie
Keyword(s):  
Markov Chains ◽  
Queueing Models ◽  
Gibbs Samplers ◽  
Reversible Markov Chains

The paper proves the statement of the title, and shows that it has useful applications in evaluating the convergence of queueing models and Gibbs samplers with deterministic and random scans.

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