On a Perturbation Method for Stochastic Parabolic PDE

Small perturbation of stochastic parabolic equations: a power series analysis

A semi-linear second-order stochastic parabolic equation is considered with coefficients, free terms, and initial condition depending on a parameter. It is shown that under some natural conditions the solution can be written as a power series in the parameter. The equations for the coefficients in the power series expansion are derived and the convergence of the power series is studied. An exam...

M ar 1 99 9 Extinction for two parabolic stochastic PDE ’ s on the lattice

It is well known that, starting with finite mass, the super-Brownian motion dies out in finite time. The goal of this article is to show that with some additional work, one can show finite time die-out for two types of systems of stochastic differential equations on the lattice Z d. For our first system, let 1/2 ≤ γ < 1, and consider non-negative solutions of du(t, x) = ∆u(t, x)dt + u γ (t, x)d...

The Stochastic Perturbation Method for Computational Mechanics

Parabolic Pde with Hysteresis

Our objective here is to describe some results on the well-posedness of initial-boundary-value problems for a nonlinear parabolic partial diierential equation with memory eeects and with general boundary conditions. The system consists of a general porous medium equation together with a family of ordinary diierential equations subject to constraints. Such a system includes a very general class ...

On a Small Elliptic Perturbation of a Backward-Forward Parabolic Problem, with Applications to Stochastic Models

We consider an elliptic PDE in two variables. As one parameter approaches zero, this PDE collapses to a parabolic one, that is forward parabolic in a part of the domain and backward parabolic in the remainder. Such problems arise naturally in various stochastic models, such as fluid models for data-handling systems and Markovmodulated queues. We employ singular perturbation methods to study the...