Large deviations for stochastic flows and their applications
The large deviation principle (LDP) is established for stochastic flows looked upon as random variables valued in some smooth Banach space and, by using the Freidlin-Wentzell estimate and Sobolev's inequality, for stochastic flows considered as the ones valued in some Frechet space well-chosen for applying the composition principle of LDP given by \textit{A. Millet}, \textit{D. Nualart} and \textit{M. Sanz} [in: Stochastic analysis, 383-395 (1991; Zbl 0728.60028)]. A \(C_{p,r}\)-LDP for anticipating stochastic differential equations is given by the composition, too. The main tool for the establishment is to generalize classical results for diffusions.
anticipating stochastic differential equations
scientific article; zbMATH DE number 1782143
scientific article