An adaptive time-stepping method based on a posteriori weak error analysis for large SDE systems

We develop an adaptive algorithm for large SDE systems, which automatically selects (quasi-)deterministic time steps for the semi-implicit Euler method, based on an a posteriori weak error estimate. Main tools to construct the a posteriori estimator are the representation of the weak approximation e...

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Bibliographic Details
Published in:Numerische Mathematik 2021-10, Vol.149 (2), p.417-462
Main Authors: Merle, Fabian, Prohl, Andreas
Format: Article
Language:English
Subjects:
Adaptive algorithms
Error analysis
Mathematical and Computational Engineering
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical Analysis
Numerical and Computational Physics
Simulation
Theoretical
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Summary:We develop an adaptive algorithm for large SDE systems, which automatically selects (quasi-)deterministic time steps for the semi-implicit Euler method, based on an a posteriori weak error estimate. Main tools to construct the a posteriori estimator are the representation of the weak approximation error via Kolmogorov’s backward equation, a priori bounds for its solution and the Clark–Ocone formula. For a certain class of SDE systems, we validate optimal weak convergence order 1 of the a posteriori estimator, and termination of the adaptive method based on it within O ( Tol - 1 ) steps.
ISSN:0029-599X
0945-3245
DOI:10.1007/s00211-021-01233-4