scholarly journals Spectrum of large random reversible Markov chains: Heavy-tailed weights on the complete graph

2011 ◽  
Vol 39 (4) ◽  
pp. 1544-1590 ◽  
Author(s):  
Charles Bordenave ◽  
Pietro Caputo ◽  
Djalil Chafaï
Keyword(s):  
Markov Chains ◽  
Complete Graph ◽  
Reversible Markov Chains ◽  
Heavy Tailed

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

Asymptotic and monotonicity properties of some repairable systems

1998 ◽  
Vol 30 (4) ◽  
pp. 1089-1110 ◽  
Author(s):  
Günter Last ◽  
Ryszard Szekli
Keyword(s):  
Markov Chains ◽  
Total Variation ◽  
Repairable Systems ◽  
Lifetime Distributions ◽  
Failure Times ◽  
Imperfect Repair ◽  
Coupling Methods ◽  
Monotonicity Properties ◽  
Heavy Tailed

The paper studies a model of repairable systems which is flexible enough to incorporate the standard imperfect repair and many other models from the literature. Palm stationarity of virtual ages, inter-failure times and degrees of repair is studied. A Loynes-type scheme and Harris recurrent Markov chains combined with coupling methods are used. Results on the weak total variation and moment convergences are obtained and illustrated by examples with IFR, DFR, heavy-tailed and light-tailed lifetime distributions. Some convergences obtained are monotone and/or at a geometric rate.

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