scholarly journals Exponential concentration inequalities for additive functionals of Markov chains

2015 ◽  
Vol 19 ◽  
pp. 440-481 ◽  
Author(s):  
Radosław Adamczak ◽  
Witold Bednorz
2016 ◽  
Vol 53 (2) ◽  
pp. 593-599 ◽  
Author(s):  
Magda Peligrad ◽  
Sergey Utev

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.


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

2015 ◽  
Vol 52 (3) ◽  
pp. 609-621 ◽  
Author(s):  
Hendrik Baumann ◽  
Werner Sandmann

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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