Dynamics for a stochastic reaction–diffusion equation with additive noise

The finite element method for a linear stochastic parabolic partial differential equation driven by additive noise

Weak exponential schemes for stochastic differential equations with additive noise

This paper develops weak exponential schemes for the numerical solution of stochastic differential equations (SDEs) with additive noise. In particular, this work provides first and second-order methods which use at each iteration the product of the exponential of the Jacobian of the drift term with a vector. The article also addresses the rate of convergence of the new schemes. Moreover, numeri...

Attractors for Stochastic Strongly Damped Plate Equations with Additive Noise

We study the asymptotic behavior of stochastic plate equations with homogeneous Neumann boundary conditions. We show the existence of an attractor for the random dynamical system associated with the equation.

Finite Element Approximation of the Linear Stochastic Wave Equation with Additive Noise

Semidiscrete finite element approximation of the linear stochastic wave equation with additive noise is studied in a semigroup framework. Optimal error estimates for the deterministic problem are obtained under minimal regularity assumptions. These are used to prove strong convergence estimates for the stochastic problem. The theory presented here applies to multi-dimensional domains and spatia...

Stochastic heat equation with white-noise drift