Semi-implicit Euler–Maruyama scheme for polynomial diffusions on the unit ball

Takuya Nakagawa, Dai Taguchi, Tomooki Yuasa

Research output: Contribution to journalArticlepeer-review


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 [29] for proving the pathwise uniqueness for some stochastic differential equation with a non-Lipschitz diffusion coefficient.

Original languageEnglish
Article number126829
JournalJournal of Mathematical Analysis and Applications
Issue number2
Publication statusPublished - Mar 15 2023


  • Degenerate and Hölder continuous diffusion coefficient
  • Polynomial diffusions on the unit ball
  • Semi-implicit Euler–Maruyama scheme

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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