Second-order neutral stochastic evolution equations with heredity

Second-order Neutral Stochastic Evolution Equations with Heredity

in a real separable Hilbert space H , where the linear (possibly multivalued) operator A : D(A) ⊂H →H is the infinitesimal generator of a strongly continuous cosine family on H , W is a K-valued Wiener process with incremental covariance given by the nuclear operator Q defined on a complete probability space (Ω, ,P) equipped with a normal filtration ( t)t≥0, φ ∈ L(Ω;Cr), and σ is an 0-measurabl...

Nonlinear stochastic evolution equations of second order with damping

Convergence of a full discretization of a second order stochastic evolution equation with nonlinear damping is shown and thus existence of a solution is established. The discretization scheme combines an implicit time stepping scheme with an internal approximation. Uniqueness is proved as well.

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Controllability of Second-Order Semilinear Impulsive Stochastic Neutral Functional Evolution Equations

Abstract second-order damped McKean-Vlasov stochastic evolution equations

second-order damped McKean-Vlasov stochastic evolution equations N.I. Mahmudov aand M.A. McKibben b,∗ aDepartment of Mathematics, Eastern Mediterranean University, Gazimagusa, TRNC, Mersin 10, TURKEY bGoucher College, Mathematics and Computer Science Department, Baltimore, MD 21204, U S A Abstract We establish results concerning the global existence, uniqueness, approximate and exact controllab...