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An Extension of the Contraction Principle

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  • J. Garcia

    (California State University Channel Islands)

Abstract

The concept of quasi-continuity and the new concept of almost compactness for a function are the basis for the extension of the contraction principle in large deviations presented here. Important equivalences for quasi-continuity are proved in the case of metric spaces. The relation between the exponential tightness of a sequence of stochastic processes and the exponential tightness of its transform (via an almost compact function) is studied here in metric spaces. Counterexamples are given to the nonmetric case. Relations between almost compactness of a function and the goodness of a rate function are studied. Applications of the main theorem are given, including to an approximation of the stochastic integral.

Suggested Citation

  • J. Garcia, 2004. "An Extension of the Contraction Principle," Journal of Theoretical Probability, Springer, vol. 17(2), pages 403-434, April.
    • Handle: RePEc:spr:jotpro:v:17:y:2004:i:2:d:10.1023_b:jotp.0000020701.20424.d8
    DOI: 10.1023/B:JOTP.0000020701.20424.d8
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    References listed on IDEAS

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    1. Eichelsbacher, Peter & Schmock, Uwe, 1998. "Exponential approximations in completely regular topological spaces and extensions of Sanov's theorem," Stochastic Processes and their Applications, Elsevier, vol. 77(2), pages 233-251, September.
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    Cited by:

    1. Jorge Garcia, 2008. "A Large Deviation Principle for Stochastic Integrals," Journal of Theoretical Probability, Springer, vol. 21(2), pages 476-501, June.

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