Hoe ding's Inequality for Uniformly Ergodic Markov Chains
نویسنده
چکیده
We provide a generalization of Hoeeding's inequality to partial sums that are derived from a uniformly ergodic Markov chain. Our exponential inequality on the deviation of these sums from their expectation is particularly useful in situations where we require uniform control on the constants appearing in the bound.
منابع مشابه
Nonasymptotic bounds on the estimation error for regenerative MCMC algorithms∗
MCMC methods are used in Bayesian statistics not only to sample from posterior distributions but also to estimate expectations. Underlying functions are most often defined on a continuous state space and can be unbounded. We consider a regenerative setting and Monte Carlo estimators based on i.i.d. blocks of a Markov chain trajectory. The main result is an inequality for the mean square error. ...
متن کاملA Geometric Approach to Ergodic Non-homogeneous Markov Chains
Inspired by the recent work of Daubechies and Lagarias on a set of matrices with convergent innnite products, we establish a new geometric approach to the classical problem of (weakly) ergodic non-homogeneous Markov chains. The existing key inequalities (related to the Hajnal inequality) in the literature are uniied in this geometric picture. A more general inequality is established. Important ...
متن کاملA regeneration proof of the central limit theorem for uniformly ergodic Markov chains
E h(x)π(dx). Ibragimov and Linnik (1971) proved that if (Xn) is geometrically ergodic, then a central limit theorem (CLT) holds for h whenever π(|h|) < ∞, δ > 0. Cogburn (1972) proved that if a Markov chain is uniformly ergodic, with π(h) < ∞ then a CLT holds for h. The first result was re-proved in Roberts and Rosenthal (2004) using a regeneration approach; thus removing many of the technicali...
متن کاملEstimation of the Entropy Rate of ErgodicMarkov Chains
In this paper an approximation for entropy rate of an ergodic Markov chain via sample path simulation is calculated. Although there is an explicit form of the entropy rate here, the exact computational method is laborious to apply. It is demonstrated that the estimated entropy rate of Markov chain via sample path not only converges to the correct entropy rate but also does it exponential...
متن کاملErgodic BSDEs Driven by Markov Chains
We consider ergodic backward stochastic differential equations, in a setting where noise is generated by a countable state uniformly ergodic Markov chain. We show that for Lipschitz drivers such that a comparison theorem holds, these equations admit unique solutions. To obtain this result, we show by coupling and splitting techniques that uniform ergodicity estimates of Markov chains are robust...
متن کامل