Discrete Approximations of Strong Solutions of Reflecting SDEs with Discontinuous Coefficients
Volume 57 / 2009
Bulletin Polish Acad. Sci. Math. 57 (2009), 169-180
MSC: 60H20, 60H99, 60F17.
DOI: 10.4064/ba57-2-10
Abstract
We study ${L}^p$ convergence for the Euler scheme for stochastic differential equations reflecting on the boundary of a general convex domain $D\subseteq\mathbb{R}^d$. We assume that the equation has the pathwise uniqueness property and its coefficients are measurable and continuous almost everywhere with respect to the Lebesgue measure. In the case $D=[0,\infty)$ new sufficient conditions ensuring pathwise uniqueness for equations with possibly discontinuous coefficients are given.
