Existence of Weak Solutions to Stochastic Evolution Inclusions

Weak Solutions of Stochastic Differential Inclusions and Their Compactness

In this paper, we consider weak solutions to stochastic inclusions driven by a semimartingale and a martingale problem formulated for such inclusions. Using this we analyze compactness of the set of solutions. The paper extends some earlier results known for stochastic differential inclusions driven by a diffusion process.

Existence of Solutions to Impulsive Fractional Partial Neutral Stochastic Integro-differential Inclusions with State-dependent Delay

We study the existence of mild solutions for a class of impulsive fractional partial neutral stochastic integro-differential inclusions with statedependent delay. We assume that the undelayed part generates a solution operator and transform it into an integral equation. Sufficient conditions for the existence of solutions are derived by using the nonlinear alternative of Leray-Schauder type for...

On the Existence of Weak Variational Solutions to Stochastic Differential Equations

We study the existence of weak variational solutions in a Gelfand triplet of real separable Hilbert spaces, under continuity, growth, and coercivity conditions on the coefficients of the stochastic differential equation. The laws of finite dimensional approximations are proved to weakly converge to the limit which is identified as a weak solution. The solution is an H– valued continuous process...

Existence of Solutions for Second Order Stochastic Differential Inclusions in Hilbert Spaces

In this paper, sufficient conditions are given for the existence of solutions for a class of second order stochastic differential inclusions in Hilbert space with the help of Leray-Schauder Nonlinear Alternative.

Existence of weak solutions in elasticity