Year: 2010
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 5 : pp. 579–605
Abstract
In an earlier paper, we proved the existence of solutions to the Skorohod problem with oblique reflection in time-dependent domains and, subsequently, applied this result to the problem of constructing solutions, in time-dependent domains, to stochastic differential equations with oblique reflection. In this paper we use these results to construct weak approximations of solutions to stochastic differential equations with oblique reflection, in time-dependent domains in $\mathbb{R}^{d}$, by means of a projected Euler scheme. We prove that the constructed method has, as is the case for normal reflection and time-independent domains, an order of convergence equal to $1/2$ and we evaluate the method empirically by means of two numerical examples. Furthermore, using a well-known extension of the Feynman-Kac formula, to stochastic differential equations with reflection, our method gives, in addition, a Monte Carlo method for solving second order parabolic partial differential equations with Robin boundary conditions in time-dependent domains.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.1003-m2957
Journal of Computational Mathematics, Vol. 28 (2010), Iss. 5 : pp. 579–605
Published online: 2010-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Stochastic differential equations Oblique reflection Robin boundary conditions Skorohod problem Time-dependent domain Weak approximation Monte Carlo method Parabolic partial differential equations Projected Euler scheme.
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