Maximum-likelihood estimates of the parameters of stochastic differential equations are consistent and asymptotically efficient, but unfortunately difficult to obtain if a closed-form expression for the transitional probability density function of the process is not available. As a result, a...

We propose an accurate data-driven numerical scheme to solve stochastic differential equations (SDEs), by taking large time steps. The SDE discretization is built up by means of the polynomial chaos expansion method, on the basis of accurately determined stochastic collocation (SC) points. By...

The main discretization schemes for diffusion processes, both unrestricted and reflecting in a hyper-rectangle, are considered. For every discretized path, an `antithetic' path is obtained by changing the sign of the driving random variables, which are chosen symmetric. It is shown that, under...

In this paper the intrinsic complex nature of engineering systems under control is treated by introducing an approach based on Controlled Stochastic Differential Equations with Markovian Switchings (in short CSDEMS). Technical conditions for the existence and uniqueness of the solutions of the...