- Date: 29 Jul. (Thu.)
- Place: On the Web
- Time: 16:30 – 18:00
- Speaker: Takuya Nakagawa (Ritsumeikan University)
- Title: Projection scheme for polynomial diffusions on the unit ball
- Abstract:
In this talk, we consider numerical schemes for polynomial diffusions on the d-dimensional unit ball, which are solutions of stochastic differential equations with a diffusion coefficient of the form (1-|x|^{2})^{1/2}. We introduce a projection scheme on the unit ball based on a backward Euler–Maruyama scheme with the projection and provide the L^{2}-rate of convergence. The main idea to consider the numerical scheme is a transformation argument introduced by Swart, J. M. (2012) for proving the pathwise uniqueness for some stochastic differential equation with a non-Lipschitz diffusion coefficient. This study is a joint work with Dai Taguchi and Tomooki Yuasa.