A SUPPORT THEOREM AND A LARGE DEVIATION PRINCIPLE FOR KUNITA FLOWS

Abstract

In this paper, stochastic flows driven by Kunita-type stochastic differential equations are studied, focusing on support theorems (ST) and large deviation principles (LDP). We establish a new ST and LDP for Brownian flows with respect to a fine Hölder topology. Our approach is based on recent advances in rough paths theory, which is the natural framework for proving ST and LDP. Nevertheless, while rigorous, our presentation stays rather clear from the rough paths technicalities and is accessible for readers not familiar with them. We view the localized Brownian stochastic flow as a projection of the solution of a rough path differential equation implying the ST and LDP. In a second step the results are generalized for the global flow.