Displaying similar documents to “Estimates on the solution of an elliptic equation related to Brownian motion with drift (II).”

Estimates on the solution of an elliptic equation related to Brownian motion with drift.

Joseph G. Conlon, Juan Redondo (1995)

Revista Matemática Iberoamericana

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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.

Joseph G. Conlon, Peder Olsen (1999)

Publicacions Matemàtiques

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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.