Now showing items 1-7 of 7
A Fleming-Viat particle representation of Dirichlet Laplacian
(Springer-Verlag GmbH, 2000-11)
We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different particle splits into two particles. For large N, the particle distribution density converges to the normalized heat equation solution in D ...
Brownian motion reflected on Brownian motion
(Springer-Verlag GmbH, 2002-04)
We study Brownian motion reflected on an "independent" Brownian path. We prove results on the joint distribution of both processes and the support of the parabolic measure in the space-time domain bounded by a Brownian path. We show that there exist two different natural local times for a Brownian path reflected on a Brownian path.
Variably skewed Brownian motion
(Institute of Mathematical Statistics, 2000-03-01)
Given a standard Brownian motion B, we show that the equation X [subscript] t = x [subscript] 0 + B [subscript] t + [beta](L [to the power of X] [subscript] t ); t [is greater than or equal to] 0 ; has a unique strong solution X. Here L [to the power of X] is the symmetric local time of X at 0, and [beta] is a given differentiable ...
The supremum of Brownian local times on Holder curves
For f : [maps the set] [0, 1] [into the set of real numbers] R, we consider L ([to the power of] f [subscript] t), the local time of spacetime Brownian motion on the curve f. Let S [subscript alpha] be the class of all functions whose Holder norm of order [alpha] is less than or equal to 1. We show that the supremum of L ...
The heat equation in time dependent domains with insulated boundaries
(Academic Press (Elsevier), 2004-10)
The paper studies, among other things, two types of possible singularities of the solution to the heat equation at the boundary of a moving domain. Several explicit results on "heat atoms" and "heat singularities" are given.
Erratum to The Supremum of Brownian Times on Hölder Curves
For [function] f [maps the set]: [0, 1] [into the set] [Real numbers], we consider L [superscript] f [subscript] t , the local time of spacetime Brownian motion on the curve f. Let S [subscript][sigma] be the class of all functions whose Hölder norm of order [sigma] is less than or equal to 1. We show that the supremum of L ...
On the Robin problem in fractal domains
We study the solution to the Robin boundary problem for the Laplacian in a Euclidean domain. We present some families of fractal domains where the infimum is greater than 0, and some other families of domains where it is equal to 0. We also give a new result on "trap domains" defined in [BCM], i.e., domains where reflecting ...