Milstein Approximation for Advection-Diffusion Equations Driven by Multiplicative Noncontinuous Martingale Noises
- ETH, Seminar fuer Angewandte Mathematik (Switzerland)
In this paper, the strong approximation of a stochastic partial differential equation, whose differential operator is of advection-diffusion type and which is driven by a multiplicative, infinite dimensional, cadlag, square integrable martingale, is presented. A finite dimensional projection of the infinite dimensional equation, for example a Galerkin projection, with nonequidistant time stepping is used. Error estimates for the discretized equation are derived in L{sup 2} and almost sure senses. Besides space and time discretizations, noise approximations are also provided, where the Milstein double stochastic integral is approximated in such a way that the overall complexity is not increased compared to an Euler-Maruyama approximation. Finally, simulations complete the paper.
- OSTI ID:
- 22092052
- Journal Information:
- Applied Mathematics and Optimization, Vol. 66, Issue 3; Other Information: Copyright (c) 2012 Springer Science+Business Media New York; Article Copyright (c) 2012 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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