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Maximum asymptotic variance of sums of finite Markov chains


  • León, Carlos A.


An optimal bound is given for the asymptotic variance of the empirical mean n-1[summation operator]1nf(Xk), where (Xk) is a finite ergodic Markov chain and f is any bounded function defined on the state space E such that the stationary mean is a fixed number [mu]. This bound depends only on [mu], [lambda] and the endpoints of the support of f(E).

Suggested Citation

  • León, Carlos A., 2001. "Maximum asymptotic variance of sums of finite Markov chains," Statistics & Probability Letters, Elsevier, vol. 54(4), pages 413-415, October.
  • Handle: RePEc:eee:stapro:v:54:y:2001:i:4:p:413-415

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    Cited by:

    1. Szewczak, Zbigniew S., 2012. "On Dobrushin’s inequality," Statistics & Probability Letters, Elsevier, vol. 82(6), pages 1202-1207.


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