A Large Deviation Principle for Stochastic Integrals

Jorge Garcia ()
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Jorge Garcia: California State University Channel Islands

Journal of Theoretical Probability, 2008, vol. 21, issue 2, 476-501

Abstract: 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.

Keywords: Stochastic integrals; Large deviations; Exponential tightness; SDE; Uniform exponential tightness; Almost compactness; Uniform controlled variations (search for similar items in EconPapers)
Date: 2008
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DOI: 10.1007/s10959-007-0136-4

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