Mathematics of Computation

Solving parabolic stochastic partial differential equations via averaging over characteristics

Author(s): G. N. Milstein; M. V. Tretyakov.
Journal: Math. Comp. 78 (2009), 2075-2106.
MSC (2000): Primary 65C30, 60H15, 60H35, 60G35
Posted: March 6, 2009
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Abstract: The method of characteristics (the averaging over the characteristic formula) and the weak-sense numerical integration of ordinary stochastic differential equations together with the Monte Carlo technique are used to propose numerical methods for linear stochastic partial differential equations (SPDEs). Their orders of convergence in the mean-square sense and in the sense of almost sure convergence are obtained. A variance reduction technique for the Monte Carlo procedures is considered. Layer methods for linear and semilinear SPDEs are constructed and the corresponding convergence theorems are proved. The approach developed is supported by numerical experiments.

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Retrieve articles in Mathematics of Computation with MSC (2000): 65C30, 60H15, 60H35, 60G35

G. N. Milstein
Affiliation: Ural State University, Lenin Str. 51, 620083 Ekaterinburg, Russia
Email: Grigori.Milstein@usu.ru

M. V. Tretyakov
Affiliation: Department of Mathematics, University of Leicester, Leicester LE1 7RH, United Kingdom
Email: M.Tretyakov@le.ac.uk

DOI: 10.1090/S0025-5718-09-02250-9
PII: S 0025-5718(09)02250-9
Keywords: Probabilistic representations of solutions of stochastic partial differential equations, numerical integration of stochastic differential equations, Monte Carlo technique, mean-square and almost sure convergence, layer methods.
Received by editor(s): May 30, 2007
Received by editor(s) in revised form: November 3, 2008
Posted: March 6, 2009
Copyright of article: Copyright 2009, American Mathematical Society

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