Weak exponential schemes for stochastic differential equations with additive noise

This paper develops weak exponential schemes for the numerical solution of stochastic differential equations (SDEs) with additive noise. In particular, this work provides first and second-order methods which use at each iteration the product of the exponential of the Jacobian of the drift term with a vector. The article also addresses the rate of convergence of the new schemes. Moreover, numerical experiments illustrate that the numerical methods introduced here are a good alternative to the standard integrators for the long time integration of SDEs whose solutions by the common explicit schemes exhibit instabilities.