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August 2007 A large deviation inequality for vector functions on finite reversible Markov Chains
Vladislav Kargin
Ann. Appl. Probab. 17(4): 1202-1221 (August 2007). DOI: 10.1214/105051607000000078

Abstract

Let SN 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 SN 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.

Citation

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Vladislav Kargin. "A large deviation inequality for vector functions on finite reversible Markov Chains." Ann. Appl. Probab. 17 (4) 1202 - 1221, August 2007. https://doi.org/10.1214/105051607000000078

Information

Published: August 2007
First available in Project Euclid: 10 August 2007

zbMATH: 1131.60067
MathSciNet: MR2344304
Digital Object Identifier: 10.1214/105051607000000078

Subjects:
Primary: 60F10, 60J10

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.17 • No. 4 • August 2007
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