Continuous extensions of numerical methods for Stochastic Fractional Differential Equations

We present a technique to provide continuous-time extension of numerical methods solving Stochastic Fractional Differential Equations (SFDEs). The basic idea we follow is closely related to the classic scenario of deterministic collocation methods for ordinary differential equations, useful to provide accurate error estimates and to perform a variable step-size implementation. The building block of this analysis is the continuous extension of Euler Maruyama method, whose effectiveness is also confirmed by selected numerical experiments. This is a joint work with B. Paternoster, R. D’Ambrosio and D. Conte.