In this note we provide a stochastic method for approximating solutions of ordinary differential equations. To this end, a stochastic variant of the Euler scheme is given by means of Markov chains. For an ordinary differential equation, these approximations are shown to satisfy a Large Number Law, and a Central Limit Theorem for the corresponding fluctuations about the solution of the differential equation is proven.
"A stochastic scheme of approximation for ordinary differential equations." Electron. Commun. Probab. 13 1 - 9, 2008. https://doi.org/10.1214/ECP.v13-1341