Adaptive concepts for high-dimensional SDE's
A talk in the BI.discrete series by
Fabian Merle from Universität Tübingen
| Abstract: | We efficiently approximate high-dimensional stochastic differential
equations (SDE's) via newly developed, theoretical-based adaptive
methods. The talk is split into two parts, which motivate and discuss
the (temporal) approximation of high-dimensional SDE's from different
aspects: in the first part we mainly consider SDE systems emerging
from a spatial discretization of a (semilinear) stochastic partial
differential equation; in the second part we consider SDE systems
which arise from the probabilistic reformulation of a given boundary
value problem. Conceptually, the derivation of the corresponding
adaptive methods follows the same principle: finding an appropriate
scheme for the approximation of the underlying SDE, derivation of a
(weak) a posteriori error estimate, and an implementation of an
adaptive method based on it. The talk is based on the joint works [1] & [2] with my supervisor Andreas Prohl in the course of my PhD. [1] F. Merle, A. Prohl, An adaptive time-stepping method based on a posteriori weak error analysis for large SDE systems, Numer. Math. 149, pp. 417-462 (2021) [2] F. Merle, A. Prohl, A posteriori error analysis and Adaptivity for high-dimensional elliptic and parabolic boundary value problems, submitted (2022) Zoom Meeting ID: 926 5310 0938 Passcode: 1928 Within the CRC this talk is associated to the project(s): A7, B7 |