Improved Simulation for the Killed Brownian Motion in a Cone

• Published in: SIAM journal on numerical analysis Vol. 44; no. 6; pp. 2610 - 2632
• Main Author: Menozzi, Stéphane
• Format: Journal Article
• Language: English
• Published: Philadelphia, PA Society for Industrial and Applied Mathematics 01-01-2006
• Subjects: Acceleration of convergence; Approximation; Brownian motion; Calculus of variations and optimal control; Correlation coefficients; Dirichlet problem; Eigenfunctions; Eigenvalues; Exact sciences and technology; Half spaces; Mathematical analysis; Mathematical extrapolation; Mathematical functions; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Ordinary differential equations; Probability; Sciences and techniques of general use; Simulation; 60J65; domain correction; Error estimation; Convergence acceleration; Differential equation; overshoot above the boundary; nonsmooth domains; Runge Kutta method; Convergence; Brownian motion; Extrapolation; Numerical analysis; 65C30; Multistep method; Convergence rate; Dirichlet problem; discretely killed Brownian motion; 60H35
• ISSN: 0036-1429; 1095-7170
• DOI: 10.1137/050636966

In this paper, we first give an error expansion of the weak error associated to a discretely killed Brownian motion in a cone that writes as an intersection of half spaces. We exploit this result to derive an original correction method to improve the initial convergence rate. This method is based on the sensitivity of the underlying Dirichlet problem w.r.t. the domain and turns out to be a numerically cheaper and sharper alternative to standard extrapolation techniques.