Homogenization of nonlocal partial differential equations related to stochastic differential equations with Lévy noise

Stochastic Homogenization of Reflected Stochastic Differential Equations

We investigate a functional limit theorem (homogenization) for Reflected Stochastic Differential Equations on a half-plane with stationary coefficients when it is necessary to analyze both the effective Brownian motion and the effective local time. We prove that the limiting process is a reflected non-standard Brownian motion. Beyond the result, this problem is known as a prototype of non-trans...

Stochastic Partial Differential Equations

HOMOGENIZATION of SYSTEMS of PARTIAL DIFFERENTIAL EQUATIONS

In this paper, we consider the class of systems of nonlinear partial differential equations, which has been lengthily studied by Prof J. FREHSE and the A. , with application to stochastic differential games with N players. In particular, we refer to the book, A.BENSOUSSAN, J. FREHSE [1]. The regularity theory is instrumental to prove the existence of equilibriums in noncooperative games. The ob...

Stochastic Partial Differential Equations with Dirichlet White-noise Boundary Conditions

– The paper is devoted to one-dimensional nonlinear stochastic partial differential equations of parabolic type with non homogeneous Dirichlet boundary conditions of white-noise type. We formulate a set of conditions that a random field must satisfy to solve the equation. We show that a unique solution exists and that we can write it in terms of the stochastic kernel related to the problem. Thi...

Stochastic Partial Differential Equations Driven by Lévy Space - Time White Noise

In this paper we develop a white noise framework for the study of stochastic partial differential equations driven by a d-parameter (pure jump) Lévy white noise. As an example we use this theory to solve the stochastic Poisson equation with respect to Lévy white noise for any dimension d. The solution is a stochastic distribution process given explicitly. We also show that if d ≤ 3, then this s...