Perturbation theory for random walk in asymmetric random environment.
Homogenization of random walk in asymmetric random environment.
On homogenization of a diffusion perturbed by a periodic reflection invariant vector field.
On homogenization of elliptic equations with random coefficients.
Green's functions for elliptic and parabolic equations with random coefficients.
On homogenization of non-divergence form partial difference equations.
Estimates on the solution of an elliptic equation related to Brownian motion with drift (II).
In this paper we continue the study of the Dirichlet problem for an elliptic equation on a domain in R3 which was begun in [5]. For R > 0 let ΩR be the ball of radius R centered at the origin with boundary ∂Ω R. The Dirichlet problem we are concerned with is the following: (-Δ - b(x).∇) u(x) = f(x), x ∈ Ω R, with zero boundary conditions ...
Estimates on the solution of an elliptic equation related to Brownian motion with drift.
In this paper we are concerned with studying the Dirichlet problem for an elliptic equation on a domain in R3. For simplicity we shall assume that the domain is a ball ΩR of radius R. Thus: ΩR = {x ∈ R3 : |x| < R}. The equation we are concerned with is given by (-Δ - b(x).∇) u(x) = f(x), x ∈ ΩR, with zero Dirichlet boundary conditions.
Fluctuations of brownian motion with drift.
Consider 3-dimensional Brownian motion started on the unit sphere {|x| = 1} with initial density ρ. Let ρt be the first hitting density on the sphere {|x| = t + 1}, t > 0. Then the linear operators T defined by T ρ = ρ form a semigroup with an infinitesimal generator which is approximately the square root of the Laplacian. This paper studies the analogous situation for Brownian motion with a drift , where is small in a suitable scale invariant norm.
Page 1