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

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

2005-08-26

arxiv.org/abs/math/0508538v3

Annals of Applied Probability 2007, Vol. 17, No. 4, 1202-1221

Mathematics

Probability

Published in at http://dx.doi.org/10.1214/105051607000000078 the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051607000000078

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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