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A Large Deviation Principle for Stochastic Integrals

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  • Jorge Garcia

    (California State University Channel Islands)

Abstract

Assuming that {(X n ,Y n )} satisfies the large deviation principle with good rate function I ♯ , conditions are given under which the sequence of triples {(X n ,Y n ,X n ⋅Y n )} satisfies the large deviation principle. An ε-approximation to the stochastic integral is proven to be almost compact. As is well known from the contraction principle, we can derive the large deviation principle when applying continuous functions to sequences that satisfy the large deviation principle; the method showed here skips the contraction principle, uses almost compactness and can be used to derive a generalization of the work of Dembo and Zeitouni on exponential approximations. An application of the main result to stochastic differential equations is given, namely, a Freidlin-Wentzell theorem is obtained for a sequence of solutions of SDE’s.

Suggested Citation

  • Jorge Garcia, 2008. "A Large Deviation Principle for Stochastic Integrals," Journal of Theoretical Probability, Springer, vol. 21(2), pages 476-501, June.
    • Handle: RePEc:spr:jotpro:v:21:y:2008:i:2:d:10.1007_s10959-007-0136-4
    DOI: 10.1007/s10959-007-0136-4
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    References listed on IDEAS

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    1. de Acosta, A., 1994. "Large deviations for vector-valued Lévy processes," Stochastic Processes and their Applications, Elsevier, vol. 51(1), pages 75-115, June.
    2. J. Garcia, 2004. "An Extension of the Contraction Principle," Journal of Theoretical Probability, Springer, vol. 17(2), pages 403-434, April.
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