Local error estimation of one-step methods for Stochastic Differential Equations

This talk highlights recent advances in the numerics of Stochastic Differential Equations (SDEs), since their applications are in several real-life phenomena, whose dynamics are affected by random perturbations. In particular, in this work we describe an efficient procedure to estimate the local truncation error of one-step method for the numerical solution of SDEs of Ito type, based on the idea of their continuous-time extension. As known in the deterministic case, this procedure allows us to obtain a variable stepsize algorithm, that may be useful to solve stiff SDEs. Numerical tests will be performed in order to confirm the theoretical results. This is a joint work with Prof. Beatrice Paternoster and Prof. Dajana Conte from University of Salerno and Prof. Raffaele D’Ambrosio from University of L’Aquila