Stochastic Volterra Equations of Nonscalar Type in Hilbert Space

Stochastic Volterra Equations of Nonscalar Type in Hilbert Space

In the paper stochastic Volterra equations of nonscalar type in Hilbert space are studied. The aim of the paper is to provide some results on stochastic convolution and mild solutions to those Volterra equations. The motivation of the paper comes from a model of aging viscoelastic materials. The pseudo-resolvent approach is used.

Stochastic Volterra Equations of Nonscalar Type

In the paper stochastic Volterra equations of nonscalar type are studied using resolvent approach. The aim of this note is to provide some results on stochastic convolution and integral mild solutions to those Volterra equations. The motivation of the paper comes from a model of aging viscoelastic materials.

On stochastic fractional Volterra equations in Hilbert space

In this paper, stochastic Volterra equations, particularly fractional, in Hilbert space are studied. Sufficient conditions for mild solutions to be strong solutions are provided. Several examples of Volterra equations having strong solutions are given, as well.

Stochastic differential inclusions of semimonotone type in Hilbert spaces

In this paper, we study the existence of generalized solutions for the infinite dimensional nonlinear stochastic differential inclusions $dx(t) in F(t,x(t))dt +G(t,x(t))dW_t$ in which the multifunction $F$ is semimonotone and hemicontinuous and the operator-valued multifunction $G$ satisfies a Lipschitz condition. We define the It^{o} stochastic integral of operator set-valued stochastic pr...

On Some Fractional Stochastic Integrodifferential Equations in Hilbert Space