scholarly journals Exponential concentration inequalities for additive functionals of Markov chains

2015 ◽  
Vol 19 ◽  
pp. 440-481 ◽  
Author(s):  
Radosław Adamczak ◽  
Witold Bednorz
Keyword(s):  
Markov Chains ◽  
Concentration Inequalities ◽  
Additive Functionals

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.

scholarly journals Transportation and concentration inequalities for bifurcating Markov chains

Bernoulli ◽  
2017 ◽  
Vol 23 (4B) ◽  
pp. 3213-3242 ◽  
Author(s):  
S. Valère Bitseki Penda ◽  
Mikael Escobar-Bach ◽  
Arnaud Guillin
Keyword(s):  
Markov Chains ◽  
Concentration Inequalities

scholarly journals Bounded truncation error for long-run averages in infinite Markov chains

2015 ◽  
Vol 52 (3) ◽  
pp. 609-621 ◽  
Author(s):  
Hendrik Baumann ◽  
Werner Sandmann
Keyword(s):  
Markov Chains ◽  
Performance Measures ◽  
Network Performance ◽  
Truncation Error ◽  
Queueing Network ◽  
Discrete State ◽  
Additive Functionals ◽  
Long Run ◽  
Special Cases ◽  
Drift Conditions

We consider long-run averages of additive functionals on infinite discrete-state Markov chains, either continuous or discrete in time. Special cases include long-run average costs or rewards, stationary moments of the components of ergodic multi-dimensional Markov chains, queueing network performance measures, and many others. By exploiting Foster-Lyapunov-type criteria involving drift conditions for the finiteness of long-run averages we determine suitable finite subsets of the state space such that the truncation error is bounded. Illustrative examples demonstrate the application of this method.

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