On large deviations for small noise Itô processes

Abstract: The large deviation principle in the small noise limit is derived for solutions of possibly degenerate It^o stochastic differential equations with predictable coefficients, which may depend also on the large deviation parameter. The result is established under mild assumptions using the Dupuis-Ellis weak convergence approach. Applications to certain systems with memory and to positive diffusions with square-root-like dispersion coefficient are included.