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2019 A Hoeffding inequality for Markov chains
Shravas Rao
Electron. Commun. Probab. 24: 1-11 (2019). DOI: 10.1214/19-ECP219

Abstract

We prove deviation bounds for the random variable $\sum _{i=1}^{n} f_i(Y_i)$ in which $\{Y_i\}_{i=1}^{\infty }$ is a Markov chain with stationary distribution and state space $[N]$, and $f_i: [N] \rightarrow [-a_i, a_i]$. Our bound improves upon previously known bounds in that the dependence is on $\sqrt{a_1^2+\cdots +a_n^2} $ rather than $\max _{i}\{a_i\}\sqrt{n} .$ We also prove deviation bounds for certain types of sums of vector–valued random variables obtained from a Markov chain in a similar manner. One application includes bounding the expected value of the Schatten $\infty $-norm of a random matrix whose entries are obtained from a Markov chain.

Citation

Download Citation

Shravas Rao. "A Hoeffding inequality for Markov chains." Electron. Commun. Probab. 24 1 - 11, 2019. https://doi.org/10.1214/19-ECP219

Information

Received: 13 September 2018; Accepted: 17 February 2019; Published: 2019
First available in Project Euclid: 21 March 2019

zbMATH: 1412.60049
MathSciNet: MR3933038
Digital Object Identifier: 10.1214/19-ECP219

Subjects:
Primary: 60F10

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