In this paper, we concentrate on a control system with non-local condition that is governed by Hilfer fractional neutral stochastic evolution hemivariational inequality (HFNSEHVI). By using concepts of the generalized Clarke sub-differential and fixed point theorem for multivalued maps, first demonstrate adequate requirements existence mild solutions to concerned system. Then, limited Lagrange ...

Existence and uniqueness for semilinear stochastic evolution equations with additive noise by means of finite-dimensional Galerkin approximations is established and the convergence rate of the Galerkin approximations to the solution of the stochastic evolution equation is estimated. These abstract results are applied to several examples of stochastic partial differential equations (SPDEs) of ev...

The topic of the talk were the time approximation of quasi linear stochastic partial differential equations of parabolic type. The framework were in the setting of stochastic evolution equations. An error bounds for the implicit Euler scheme was given and the stability of the scheme were considered.

The controllability of semilinear stochastic delay evolution equations is studied by using a stochastic version of the well-known Banach fixed point theorem and semigroup theory. An application to stochastic partial differential equations is given. 1. Introduction. The fixed point technique is widely used as a tool to study the controllability of nonlinear systems in finite-and infinite-dimensi...

The evolution of the probability density of a biological population is described using nonlinear stochastic differential equations for the growth process and the related Fokker-Planck equations for the time-dependent probability densities. It is shown that the effect of the initial conditions disappears rapidly from the evolution of the mean of the process. But the behaviour of the variance dep...

In this study, a population of evolutionary biological networks is described by a stochastic dynamic system with intrinsic random parameter fluctuations due to genetic variations and external disturbances caused by environmental changes in the evolutionary process. Since information on environmental changes is unavailable and their occurrence is unpredictable, they can be considered as a game p...

In this paper we consider structurally damped plate and wave equations with point and distributed random forces. In order to treat space dimensions more than one, we work in the setting of L–spaces with (possibly small) q ∈ (1, 2). We establish existence, uniqueness and regularity of mild and weak solutions to the stochastic equations employing recent theory for stochastic evolution equations i...