A nonlinear integration by parts formula for stochastic differential equations

11.11.2019, 12:15  –  Campus Golm Haus 9 Raum 2.22
Forschungsseminar Wahrscheinlichkeitstheorie

Sara Mazzonetto

In this talk we introduce a nonlinear integration-by-parts formula for stochastic differential equations. We call it Itô-Alekseev-Gröbner formula because it generalizes both Itô formula and the classical Alekseev-Gröbner lemma for deterministic differential equations. We focus on the fact that the formula yields a (new) perturbation theory. In other words, it allows to estimate the global error between the exact solution of an SDE and a general Itô process in terms of the local characteristics (and their Malliavin derivatives).

In the result we assume the existence of a twice differentiable flow. How restrictive is this assumption? If time permits we also discuss possible applications for deriving strong convergence rates for perturbations or approximations of stochastic (partial) differential equations.

This talk is based on joint works with A. Hudde, M. Hutzenthaler, and A. Jentzen.