In this article, we consider numerical schemes for polynomial diffusions on the unit ball, which are solutions of stochastic differential equations with a diffusion coefficient of the form 1−|x|2. We introduce a semi-implicit Euler–Maruyama scheme with the projection onto the unit ball and provide the L2-rate of convergence. The main idea to consider the numerical scheme is the transformation argument introduced by Swart  for proving the pathwise uniqueness for some stochastic differential equation with a non-Lipschitz diffusion coefficient.
- Degenerate and Hölder continuous diffusion coefficient
- Polynomial diffusions on the unit ball
- Semi-implicit Euler–Maruyama scheme
ASJC Scopus subject areas
- Applied Mathematics