We study stochastic differential equations with jumps with no diffusion part. We provide some basic stochastic characterizations of solutions of the corresponding non-local partial differential equations and prove the Harnack inequality for a class of these operators. We also establish key connections between the recurrence properties of these jump processes and the non-local partial differenti...

Random invariant manifolds often provide geometric structures for understanding stochastic dynamics. In this paper, a dynamical approximation estimate is derived for a class of stochastic partial differential equations, by showing that the random invariant manifold is almost surely asymptotically complete. The asymptotic dynamical behavior is thus described by a stochastic ordinary differential...

We study the “periodic homogenization” for a class of nonlocal partial differential equations parabolic-type with rapidly oscillating coefficients, related to stochastic driven by multiplicative isotropic ?-stable Lévy noise (1<?<2) which is nonlinear in component. Our homogenization method probabilistic. It turns out that, under suitable regularity assumptions, limit solutions satisfies equati...

We establish a large deviation principle for the solutions of stochastic partial differential equations for nonlinear vibration of elastic panels (also called stochastic nonlinear beam equations).

A new class of random partial differential equations of parabolic type is considered where the stochastic term consists in an irregular noisy drift, not necessarily Gaussian, for which a suitable interpretation is provided. After freezing a realization of the drift (stochastic process), we study existence and uniqueness (in some appropriate sense) of the associated parabolic equation and a prob...

in this paper, we intend to solve special kind of ordinary differential equations which is called heun equations, by converting to a corresponding stochastic differential equation(s.d.e.). so, we construct a stochastic linear equation system from this equation which its solution is based on computing fundamental matrix of this system and then, this s.d.e. is solved by numerically methods. mo...