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Large Deviations for a Class of Anticipating Stochastic Differential Equations
Millet, A. Nualart, David Sanz, Marta
Millet, A.
Nualart, David
Sanz, Marta
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Abstract
Consider the family of perturbed stochastic differential equations on Rd, Xεt=Xε0+ε√∫t0σ(Xεs)∘dWs+∫t0b(Xεs)ds, ε>0, defined on the canonical space associated with the standard k-dimensional Wiener process W. We assume that {Xε0,ε>0} is a family of random vectors not necessarily adapted and that the stochastic integral is a generalized Stratonovich integral. In this paper we prove large deviations estimates for the laws of {Xε.,ε>0}, under some hypotheses on the family of initial conditions {Xε0,ε>0}.
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This is the published version, also available here: http://dx.doi.org/10.1214/aop/1176989535.
Date
1992-10-02
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Institute of Mathematical Statistics (IMS)
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Keywords
Large deviations, anticipating stochastic differential equations, stochastic flows
Citation
Millet, A.; Nualart, D.; Sanz, M. Large Deviations for a Class of Anticipating Stochastic Differential Equations. Ann. Probab. 20 (1992), no. 4, 1902--1931. http://dx.doi.org/10.1214/aop/1176989535.