We present and analyse two implicit methods for Ito stochastic differential equations (SDEs) with Poisson-driven jumps. The first method, SSBE, is a split-step extension of the backward Euler method.â€¦ (More)

A class of implicit methods is introduced for Ito stochastic differential equations with Poisson-driven jumps. A convergence proof shows that these implicit methods share the same finite time strongâ€¦ (More)

The numerical solution of stochastic partial differential equations (SPDEs) is at a stage of development roughly similar to that of stochastic ordinary differential equations (SODEs) in the 1970s,â€¦ (More)

Under a one-sided dissipative Lipschitz condition on its drift, a stochastic evolution equation with additive noise of the reaction-diffusion type is shown to have a unique stochastic stationaryâ€¦ (More)

Random ordinary differential equations (RODEs) are ordinary differential equations (ODEs) with a stochastic process in their vector field. They can be analysed pathwise using deterministic calculus,â€¦ (More)

We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of aâ€¦ (More)

We obtain regularity results for solutions of the three dimensional system of globally modified Navier-Stokes equations, and we investigate the relationship between global attractors, invariantâ€¦ (More)

Various types of attractors are considered and compared for nonautonomous dynamical systems involving a cocycle state space mapping that is driven by an autonomous dynamical system on a compactâ€¦ (More)

The Milstein scheme is the simplest nontrivial numerical scheme for stochastic differential equations with a strong order of convergence one. The scheme has been extended to the stochastic delayâ€¦ (More)