TY - JOUR
T1 - Weak Approximation of Obliquely Reflected Diffusions on Time-Dependent Domains
AU - Kaj Nyström & Thomas Önskog
JO - Journal of Computational Mathematics
VL - 5
SP - 579
EP - 605
PY - 2010
DA - 2010/10
SN - 28
DO - http://doi.org/10.4208/jcm.1003-m2957
UR - https://global-sci.org/intro/article_detail/jcm/8539.html
KW - 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.
AB - <p style="text-align: justify;">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.</p>