Sonja Cox: Sharp bounds for parameter-dependent stochastic integrals

Speaker
Sonja Cox, Univ. of Amsterdam

Abstract
We provide sharp bounds in the supremum- and Hölder norm for parameter-dependent stochastic integrals. As an application we obtain novel long-term bounds for stochastic partial differential equations as well as novel bounds on the space-time modulus of continuity of the stochastic heat equation. I will also explain how these bounds were used in recent work of Klioba and Veraar to obtain optimal (not just essentially optimal) convergence rates for temporal discretizations of SPDEs. This talk concerns joint work with Joris van Winden (TU Delft).