Euler Approximation for A Class of Singular Multi-Dimensional SDEs Driven by an Additive Fractional Noise

Abstract

We consider a class of multi-dimensional stochastic differential equations driven by fractional Brownian motion with Hurst index . In particular, the drift coefficient blows up at 0. We first prove that this equation has a unique positive solution, and then propose a semi-implicit Euler approximation scheme for the equation, and finally show that it is also positive, and study its rate of convergence.