Study of a Brownian impulse

Abstract

This paper is concerned with the simulation of a 2-dimensional stochastic differential equation motivated by some physical phenomena of fluid mechanics. The drift and diffusion coefficients of the equation admitting local singularities, we are led to study a particular term of strong perturbation denoted by “Brownian impulse.” Our suggestion for the simulation is to replace the singularity by a jump on which our study therefore focuses.