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Compactness in the theory of large deviations

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  • O'Brien, George L.
  • Vervaat, Wim

Abstract

Large-deviation principles (LDPs) are expressed as the vague or narrow convergence of sequences of set functions called capacities. Compactness and other topological properties of the collection of capacities are then used in conjunction with Varadhan's integral theorem to reduce the proof of LDPs to the problem of showing that a certain system of equations has a unique solution. As applications of these ideas, we present short proofs of extended versions of a theorem of Bryc and of the Gärtner-Ellis theorem.

Suggested Citation

  • O'Brien, George L. & Vervaat, Wim, 1995. "Compactness in the theory of large deviations," Stochastic Processes and their Applications, Elsevier, vol. 57(1), pages 1-10, May.
    • Handle: RePEc:eee:spapps:v:57:y:1995:i:1:p:1-10
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    Cited by:

    1. Nyrhinen, Harri, 2007. "Convex large deviation rate functions under mixtures of linear transformations, with an application to ruin theory," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 947-959, July.
    2. Ganguly, Arnab, 2018. "Large deviation principle for stochastic integrals and stochastic differential equations driven by infinite-dimensional semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 128(7), pages 2179-2227.

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