In this paper we explain the notion of stochastic backward differential equations and its relationship with classical (backward) parabolic differential equations of second order. The paper contains a mixture of stochastic processes like Markov processes and martingale theory and semi-linear partial differential equations of parabolic type. Some emphasis is put on the fact that the whole theory ...

This work is concerned with a Freidlin--Wentzell type large deviation principle for family of multiscale quasilinear and semilinear stochastic partial differential equations. Employing the weak c...

We investigate the approximate controllability property for a class of linear stochastic equations driven by independent Brownian motion and Poisson random measure. The paper generalizes recent results of Buckdahn et al. (2006, A characterization of approximately controllable linear stochastic differential equations. Stochastic Partial Differential Equations and Applications (G. Da Prato & L. T...