Stochastic variational inequalities and regularity for degenerate stochastic partial differential equations

Stochastic Partial Differential Equations with Unbounded and Degenerate Coefficients

Abstract. In this article, using DiPerna-Lions theory [1], we investigate linear second order stochastic partial differential equations with unbounded and degenerate non-smooth coefficients, and obtain several conditions for existence and uniqueness. Moreover, we also prove the L1integrability and a general maximal principle for generalized solutions of SPDEs. As applications, we study nonlinea...

Degenerate Parabolic Stochastic Partial Differential Equations: Quasilinear case

In this paper, we study the Cauchy problem for a quasilinear degenerate parabolic stochastic partial differential equation driven by a cylindrical Wiener process. In particular, we adapt the notion of kinetic formulation and kinetic solution and develop a well-posedness theory that includes also an L1-contraction property. In comparison to the previous works of the authors concerning stochastic...

Stochastic Partial Differential Equations

Degenerate Stochastic Differential Equations, Flows and Hypoellipticity

Stochastic differential equations and integrating factor

The aim of this paper is the analytical solutions the family of rst-order nonlinear stochastic differentialequations. We dene an integrating factor for the large class of special nonlinear stochasticdierential equations. With multiply both sides with the integrating factor, we introduce a deterministicdierential equation. The results showed the accuracy of the present work.