Related papers: A Hoeffding inequality for Markov chains

Let $\{Y_i\}_{i=1}^{\infty}$ be a stationary reversible Markov chain with state space $[N]$, let $(X, \| \cdot \|)$ be a real-valued Banach space and let $f_1, \ldots, f_n: [N] \rightarrow X$ be functions with mean $0$ such that $\|f_i(v)\|…

We build optimal exponential bounds for the probabilities of large deviations of sums \sum_{k=1}^nf(X_k) where (X_k) is a finite reversible Markov chain and f is an arbitrary bounded function. These bounds depend only on the stationary mean…

We extend Hoeffding's lemma to general-state-space and not necessarily reversible Markov chains. Let $\{X_i\}_{i \ge 1}$ be a stationary Markov chain with invariant measure $\pi$ and absolute spectral gap $1-\lambda$, where $\lambda$ is…

We consider Markov chain with spectral gap in $L^2$ space. Assume that $f$ is a bounded function. Then the probabilities of large deviations of average along trajectory satisfy Hoeffding's-type inequalities. These bounds depend only on the…

This paper develops an optimal Chernoff type bound for the probabilities of large deviations of sums $\sum_{k=1}^n f (X_k)$ where $f$ is a real-valued function and $(X_k)_{k \in \mathbb{Z}_{\ge 0}}$ is a finite state Markov chain with an…

This paper develops a Hoeffding inequality for the partial sums $\sum_{k=1}^n f (X_k)$, where $\{X_k\}_{k \in \mathbb{Z}_{> 0}}$ is an irreducible Markov chain on a finite state space $S$, and $f : S \to [a, b]$ is a real-valued function.…

Let $S_N$ be the sum of vector-valued functions defined on a finite Markov chain. An analogue of the Bernstein--Hoeffding inequality is derived for the probability of large deviations of $S_N$ and relates the probability to the spectral gap…

The partial sum of the states of a Markov chain or more generally a Markov source is asymptotically normally distributed under suitable conditions. One of these conditions is that the variance is unbounded. A simple combinatorial…

We give Hoeffding and Bernstein-type concentration inequalities for the largest eigenvalue of sums of random matrices arising from a Markov chain. We consider time-dependent matrix-valued functions on a general state space, generalizing…

We prove a Chernoff-type bound for sums of matrix-valued random variables sampled via a regular (aperiodic and irreducible) finite Markov chain. Specially, consider a random walk on a regular Markov chain and a Hermitian matrix-valued…

We provide a systematic approach to deal with the following problem. Let $X_1,\ldots,X_n$ be, possibly dependent, $[0,1]$-valued random variables. What is a sharp upper bound on the probability that their sum is significantly larger than…

In this paper, we are interested in investigating the perturbation bounds for the stationary distributions for discrete-time or continuous-time Markov chains on a countable state space. For discrete-time Markov chains, two new norm-wise…

This paper studies Hoeffding's inequality for Markov chains under the generalized concentrability condition defined via integral probability metric (IPM). The generalized concentrability condition establishes a framework that interpolates…

We use the $f-divergence$ also called relative entropy as a measure of diversity between probability densities and review its basic properties. In the sequence we define a few objects which capture relevant information from the sample of a…

Convergence rates of Markov chains have been widely studied in recent years. In particular, quantitative bounds on convergence rates have been studied in various forms by Meyn and Tweedie [Ann. Appl. Probab. 4 (1994) 981-1101], Rosenthal…

Markov chains are fundamental models for stochastic dynamics, with applications in a wide range of areas such as population dynamics, queueing systems, reinforcement learning, and Monte Carlo methods. Estimating the transition matrix and…

Hoeffding's inequality is a fundamental tool widely applied in probability theory, statistics, and machine learning. In this paper, we establish Hoeffding's inequalities specifically tailored for an irreducible and positive recurrent…

Let $\{W_t\}_{t=1}^{\infty}$ be a finite state stationary Markov chain, and suppose that $f$ is a real-valued function on the state space. If $f$ is bounded, then Gillman's expander Chernoff bound (1993) provides concentration estimates for…

We prove the first Chernoff-Hoeffding bounds for general nonreversible finite-state Markov chains based on the standard L_1 (variation distance) mixing-time of the chain. Specifically, consider an ergodic Markov chain M and a weight…

The paper is concerned with approximating the distribution of a sum W of n integer valued random variables Y_i, whose distributions depend on the state of an underlying Markov chain X. The approximation is in terms of a translated Poisson…