Semi-implicit Milstein approximation scheme for non-colliding particle systems

TL;DR

This paper proposes a semi-implicit Milstein scheme for non-colliding particle systems with non-constant diffusion, demonstrating convergence at order 1 in mean-square sense.

Contribution

It introduces a novel semi-implicit Milstein approximation for complex particle systems with proven convergence rate.

Findings

Scheme converges at order 1 in mean-square sense

Applicable to systems with non-constant diffusion coefficients

Enhances numerical simulation accuracy for non-colliding particles

Abstract

We introduce a semi-implicit Milstein approximation scheme for some class of non-colliding particle systems modeled by systems of stochastic differential equations with non-constant diffusion coefficients. We show that the scheme converges at the rate of order 1 in the mean-square sense.