Costantini, C.; Pacchiarotti, B.; Sartoretto, F. Numerical approximation for functionals of reflecting diffusion processes. (English) Zbl 0913.60031 SIAM J. Appl. Math. 58, No. 1, 73-102 (1998). Summary: The aim of this paper is to approximate the expectation of a large class of functionals of the solution \((X,\xi)\) of a stochastic differential equation with normal reflection in a piecewise smooth domain of \(\mathbb{R}^{d}\). This also yields a Monte Carlo method for solving partial differential problems of parabolic type with mixed boundary conditions. The approximation is based on a modified Euler scheme for the stochastic differential equation. The scheme can be driven by a sequence of bounded independently and identically distributed (i.i.d.) random variables, or, when the domain is convex, by a sequence of Gaussian i.i.d. random variables. The order of (weak) convergence for both cases is given. In the former case the order of convergence is 1/2, and it is shown to be exact by an example. In the last section numerical tests are presented. The behavior of the error as a function of the final time \(T\), for fixed values of the discretization step, and as a function of the discretization step, for fixed values of the final time \(T\), is analyzed. Cited in 1 ReviewCited in 19 Documents MSC: 60F17 Functional limit theorems; invariance principles 60H30 Applications of stochastic analysis (to PDEs, etc.) 65C05 Monte Carlo methods 60J50 Boundary theory for Markov processes Keywords:stochastic differential equations with reflection; reflecting boundary conditions; Neumann boundary conditions; mixed boundary conditions; numerical schemes; weak convergence; Monte Carlo method PDFBibTeX XMLCite \textit{C. Costantini} et al., SIAM J. Appl. Math. 58, No. 1, 73--102 (1998; Zbl 0913.60031) Full Text: DOI