Journal ArticleDOI
Moment and probability inequalities for sums of bounded additive functionals of regular Markov chains via the Nummelin splitting technique
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In this paper, the authors obtained Rosenthal-type inequalities and an estimate for large deviation probabilities in the case of bounded additive functionals of a Markov chain under regularity assumptions via the Nummelin splitting technique.About:
This article is published in Statistics & Probability Letters.The article was published on 2001-12-01. It has received 37 citations till now. The article focuses on the topics: Markov chain & Additive Markov chain.read more
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Book ChapterDOI
General irreducible Markov chains and non-negative operators: Notes and comments
TL;DR: In this article, the Harris recurrent Markov chains were studied and the following limit theorems were defined: 1. Irreducible kernels 3. Transience and recurrence 4. Embedded renewal processes 5. Positive and null recurrence 6. Total variation limit theorem 7.
Journal ArticleDOI
Regenerative block bootstrap for Markov chains
TL;DR: In this article, a specific bootstrap method is introduced for positive recurrent Markov chains, based on the regenerative method and the Nummelin splitting technique, which mainly consists in dividing the sample path of the chain into data blocks corresponding to the successive visits to the atom and resampling the blocks until the (random) length of the reconstructed trajectory is at least n.
Journal ArticleDOI
Nonasymptotic bounds on the estimation error of MCMC algorithms
TL;DR: This work addresses the problem of upper bounding the mean square error of MCMC estimators and establishes a general result valid for essentially all ergodic Markov chains encountered in Bayesian computation and a possibly unbounded target function f.
Journal ArticleDOI
Edgeworth expansions of suitably normalized sample mean statistics for atomic Markov chains
TL;DR: In this article, the problem of estimating functionals of type μ(f)=∫fdμ from observations drawn from a positive recurrent atomic Markov chain was studied, and the properties of different estimators were studied.
Journal ArticleDOI
Nonasymptotic bounds on the estimation error of MCMC algorithms
TL;DR: In this paper, a non-asymptotic analysis of MCMC estimators is presented for geometrically and polynomially ergodic Markov chains.
References
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Book ChapterDOI
Probability Inequalities for sums of Bounded Random Variables
TL;DR: In this article, upper bounds for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt are derived for certain sums of dependent random variables such as U statistics.
Book
Markov Chains and Stochastic Stability
Sean P. Meyn,Richard L. Tweedie +1 more
TL;DR: This second edition reflects the same discipline and style that marked out the original and helped it to become a classic: proofs are rigorous and concise, the range of applications is broad and knowledgeable, and key ideas are accessible to practitioners with limited mathematical background.
Book
Sums of Independent Random Variables
TL;DR: In this paper, the authors define the notion of infinitely divisible distributions as the limits of the distributions of sums of independent random variables, and show that the distribution of a sum of independent non-identically distributed random variables converges to a given infinitely-divisible distribution.