Self-normalized Large Deviations for Markov Chains

Mathieu Faure

doi:10.1214/EJP.v7-122

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Home > Journals > Electron. J. Probab. > Volume 7 > Article

2002 Self-normalized Large Deviations for Markov Chains

Mathieu Faure

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Mathieu Faure¹
¹Universit'e de Marne La Vall'ee

Electron. J. Probab. 7: 1-31 (2002). DOI: 10.1214/EJP.v7-122

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Abstract

We prove a self-normalized large deviation principle for sums of Banach space valued functions of a Markov chain. Self-normalization applies to situations for which a full large deviation principle is not available. We follow the lead of Dembo and Shao [DemSha98b] who state partial large deviations principles for independent and identically distributed random sequences.