Projection scheme for polynomial diffusions on the unit ball

04/08/2021

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by   Takuya Nakagawa, et al.

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In this article, we consider numerical schemes for polynomial diffusions on the unit ball ℬ^d, which are solutions of stochastic differential equations with a diffusion coefficient of the form √(1-|x|^2). We introduce a projection scheme on the unit ball ℬ^d based on a backward Euler–Maruyama scheme and provide the L^2-rate of convergence. The main idea to consider the numerical scheme is the transformation argument introduced by Swart [29] for proving the pathwise uniqueness for some stochastic differential equation with a non-Lipschitz diffusion coefficient.