Euler's Approximations of Solutions of Reflecting SDEs with Discontinuous Coefficients
Volume 61 / 2013
Bulletin Polish Acad. Sci. Math. 61 (2013), 79-85
MSC: 60H20, 60H99, 60F17.
DOI: 10.4064/ba61-1-9
Abstract
Let $D$ be either a convex domain in $\mathbb{R}^d$ or a domain satisfying the conditions (A) and (B) considered by Lions and Sznitman (1984) and Saisho (1987). We investigate convergence in law as well as in ${L}^p$ for the Euler and Euler–Peano schemes for stochastic differential equations in $D$ with normal reflection at the boundary. The coefficients are measurable, continuous almost everywhere with respect to the Lebesgue measure, and the diffusion coefficient may degenerate on some subsets of the domain.
