The $C^{0,1}$ Itô-Ventzell formula for weak Dirichlet processes

Abstract: This paper proves an extension of the It^o-Ventzell formula that applies to stochastic flows in $C^{0,1}$ for continuous weak Dirichlet processes. We apply this theorem, for example, to give a representation result for strong solutions of time-dependent elliptic SPDEs, to derive formulas for quadratic variations, and to relax assumptions in a financial mathematics context.