A backward Ito-Ventzell formula with an application to stochastic interpolation

We discuss a novel backward Ito-Ventzell formula and an extension of the Aleeksev-Gröbner interpolating formula to stochastic flows. We also present some natural spectral conditions that yield direct and simple proofs of time uniform estimates of the difference between the two stochastic flows when their drift and diffusion functions are not the same, yielding what seems to be the first results of this type for this class of  anticipative models.

We illustrate the impact of these results in the context of diffusion perturbation theory, interacting diffusions and discrete time approximations.