Euler's Approximations of Solutions of Reflecting SDEs with Discontinuous Coefficients

Alina Semrau-Giłka¹

¹ Institute of Mathematics and Physics University of Technology and Life Sciences Kaliskiego 7 85-796 Bydgoszcz, Poland

Bulletin of the Polish Academy of Sciences. Mathematics, Tome 61 (2013) no. 1, pp. 79-85.

Résumé

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.

Détail

DOI : 10.4064/ba61-1-9

Keywords: either convex domain mathbb domain satisfying conditions considered lions sznitman saisho investigate convergence law euler euler peano schemes stochastic differential equations normal reflection boundary coefficients measurable continuous almost everywhere respect lebesgue measure diffusion coefficient may degenerate subsets domain