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On large deviation principles in metric spaces

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Abstract

Many articles deal with large deviation principles (LDPs) (see [1-4] for instance and the references in [3,4]), studying mainly the LDP for the sums of random elements or for various stochastic models and dynamical systems. For a sequence of random elements in a metric space, in studying LDPs it turns out natural to introduce the concepts of the local LDP and extended LDP. They enable us to state and prove LDP-type statements in those cases when the usual LDP (cf. [3,4]) fails (see [5,6] and Section 6 of this article). We obtain conditions for the fulfillment of the extended LDP in metric spaces. The main among these conditions is the fulfillment of the local LDP. The latter is usually much simpler to prove than the extended LDP.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk, Russia

    A.A. Borovkov & A.A. Mogul’skii

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  1. A.A. Borovkov
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  2. A.A. Mogul’skii
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Correspondence to A.A. Borovkov.

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Original Russian Text Copyright © 2010 Borovkov A. A. and Mogul’skii A. A.

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Borovkov, A., Mogul’skii, A. On large deviation principles in metric spaces. Sib Math J 51, 989–1003 (2010). https://doi.org/10.1007/s11202-010-0098-0

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  • DOI: https://doi.org/10.1007/s11202-010-0098-0

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