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A large deviation inequality for vector functions on finite reversible Markov Chains

Vladislav Kargin
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Abstract

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 of the Markov chain. Examples suggest that this inequality is better than alternative inequalities if the chain has a sufficiently large spectral gap and the function is high-dimensional.

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BibTeXRIS

Vladislav Kargin. 2007-10-23. A large deviation inequality for vector functions on finite reversible Markov Chains. https://doi.org/10.1214/105051607000000078

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