Conference abstracts

Session A7 - Stochastic Computation

July 10, 15:30 ~ 15:55

Weak convergence rates for stochastic partial differential equations with nonlinear diffusion coefficients

Ryan Kurniawan

ETH Zurich, Switzerland   -   ryan.kurniawan@sam.math.ethz.ch

Strong convergence rates for numerical approximations of semilinear stochastic partial differential equations (SPDEs) with smooth and regular nonlinearities are well understood in the literature. Weak convergence rates for numerical approximations of such SPDEs have been investigated for about two decades and are still not yet fully understood. In particular, it has been an open problem to establish essentially sharp weak convergence rates for numerical approximations of space-time white noise driven SPDEs with nonlinear multiplication operators in the diffusion coefficients. In this talk we overcome this weak convergence problem. In particular, we establish essentially sharp weak convergence rates for numerical approximations of the continuous version of the parabolic Anderson model. Key ingredients of our approach are applications of the mild Ito type formula in UMD Banach spaces with type 2.

Joint work with Daniel Conus (Lehigh University, USA), Mario Hefter (TU Kaiserslautern, Germany) and Arnulf Jentzen (ETH Zurich, Switzerland).

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FoCM 2017, based on a nodethirtythree design.