The ergodic properties of SDEs, and various time discretizations for SDEs, are studied. The ergodicity of SDEs is established by using techniques from the theory of Markov chains on general state… (More)

Traditional finite-time convergence theory for numerical methods applied to stochastic differential equations (SDEs) requires a global Lipschitz assumption on the drift and diffusion coefficients. In… (More)

Numerical approximation of the long time behavior of a stochastic differential equation (SDE) is considered. Error estimates for time-averaging estimators are obtained and then used to show that the… (More)

We study the problem of parameter estimation for time-serie possessing two, widely separated, characteristic time scales. The aim is to understand situations where it is desirable to fit a… (More)

Waveform relaxation algorithms for partial di erential equations PDEs are tradi tionally obtained by discretizing the PDE in space and then splitting the discrete operator using matrix splittings For… (More)

A class of nonlinear dissipative partial diierential equations that possess nite dimensional attractive invariant manifolds is considered. An existence and perturbation theory is developed which… (More)

Two degenerate SDEs arising in statistical physics are studied. The first is a Langevin equation with state-dependent noise and damping. The second is the equation of motion for a particle obeying… (More)

We consider the inverse problem of determining the permeability from the pressure in a Darcy model of flow in a porous medium. Mathematically the problem is to find the diffusion coefficient for a… (More)