Now showing items 21-30 of 32
On the time and direction of stochastic bifurcation
This paper is a mathematical companion to an article introducing a new economics model, by Burdzy, Frankel and Pauzner (1997). The motivation of this paper is applied, but the results may have some mathematical interest in their own right. Our model, i.e., equation (1.1) below, does not seem to be known in literature. Despite ...
Positivity of Brownian transition densities
(Electronic Journal of Probability, 1997-09-24)
Let B be a Borel subset of R [to the power of] d and let p(t, x, y) be the transition densities of Brownian motion killed on leaving B. Fix x and y in B. If p(t, x, y) is positive for one t, it is positive for every value of t. Some related results are given.
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.
On Brownian Excursions in Lipschitz Domains. Part II: Local Asymptotic Distributions
(Birkhäuser Boston, Inc., 1989)
In this paper, we continue the study initiated in Burdzy and Williams (1986) of the local properties of Brownian excursions in Lipschitz domains. The focus in part I was on local path properties of such excursions. In particular, a necessary and sufficient condition was given for Brownian excursions in a Lipschitz domain to ...
Minimal Fine Derivatives and Brownian Excursions
(Nagoya University, 1990-09)
Let f be an analytic function defined on D [is a subset of] [complex numbers] C. If [the derivative of the function f at the point x] has a limit when [the set] x [into the set] z [is an element of the set partial derivative] D in the minimal fine topology then the limit will be called a minimal fine derivative. Several ...
A critical case for Brownian slow points
(Springer-Verlag GmbH, 1996-01)
Let X [subscript] t be a Brownian motion and let S(c) be the set of reals r [is greather than or equal to] 0 such that |X ([subscript] r+t) − X [subscript] r| [is less than or equal to] c [square root of] t, 0 [is less than or equal to] t [is less than or equal to] h, for some h = h(r) > 0. It is known that S(c) is empty if ...
Eigenvalue expansions for Brownian motion with an application to occupation times
(Institute of Mathematical Statistics, 1996-01-31)
Let B be a Borel subset of R [to the power of] d with finite volume. We give an eigenvalue expansion for the transition densities of Brownian motion killed on exiting B. Let A [subscript] 1 be the time spent by Brownian motion in a closed cone with vertex 0 until time one. We show that lim [subscript] u [approaching] 0 log P ...
Geometric Properties of 2-dimensional Brownian Paths
(Springer-Verlag GmbH, 1989)
Let A be the set of all points of the plane C, visited by two-dimensional Brownian motion before time 1. With probability 1, all points of A are "twist points" except a set of harmonic measure zero. "Twist points" may be continuously approached in [the set that contains all those elements of complex numbers that are not in] ...
Labyrinth dimension of Brownian trace
(Institute of Mathematics, 1995)
Suppose that X is a two-dimensional Brownian motion. The trace X[0, 1] contains a self-avoiding continuous path whose Hausdorff dimension is equal to 2.
2-D Brownian motion in a system of reflecting barriers: effective diffusivity by a sampling method
(Institute of Physics, 1994-02-07)
We study two-dimensional Brownian motion in an ordered periodic system of linear reflecting barriers using the sampling method and conformal transformations. We calculate the effective diffusivity for the Brownian particle. When the periods are fixed but the length of the barrier goes to zero, the effective diffusivity in ...