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.
"Study of a Brownian impulse." Ann. Appl. Probab. 10 (2) 493 - 516, May 2000. https://doi.org/10.1214/aoap/1019487352