Now showing items 31-40 of 84
Intersection local time for points of infinite multiplicity
(Institute of Mathematical Statistics, 1994-04)
For each a [is an element of the set] (0, 1/2), there exists a random measure [beta] [subscript] a which is supported on the set of points where two-dimensional Brownian motion spends a units of local time. The measure [beta] [subscript] a is carried by a set which has Hausdorff dimension equal to 2−a. A Palm measure ...
Fiber Brownian motion and the "hot spots" problem
(Duke University Press, 2000-10)
We show that in some planar domains both extrema of the second Neumann eigenfunction lie strictly inside the domain. The main technical innovation is the use of "fiber Brownian motion," a process which switches between two-dimensional and one-dimensional evolution.
Local time flow related to skew Brownian motion
(Institute of Mathematical Statistics, 2001-10)
We define a local time flow of skew Brownian motions, i.e., a family of solutions to the stochastic differential equation defining the skew Brownian motion, starting from different points but driven by the same Brownian motion. We prove several results on distributional and path properties of the flow. Our main result is a ...
2-D Brownian motion in a system of traps: Application of conformal transformations
(Institute of Physics, 1992)
We study two-dimensional Brownian motion in a periodic system of traps using conformal transformations. The system is periodic in the x and y directions. We calculate the ratio of the drift along the y-axis to the drift along the x-axis. The drift of the Brownian particle is induced by conditioning and by the asymmetry of the ...
Diffusion on curved, periodic surfaces
(American Physical Society, 1999-07)
We present a simulation algorithm for a diffusion on a curved surface given by the equation [omega](r)50. The algorithm is tested against analytical results known for diffusion on a cylinder and a sphere, and applied to the diffusion on the P, D, and G periodic nodal surfaces. It should find application in an interpretation ...
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 ...
A three-dimensional Brownian path reflected on a Brownian path is a free Brownian path
(Springer Science+Business Media B.V., 1993)
Three-dimensional Brownian path reflected on Brownian path is a free Brownian path.
The Martin boundary in non-Lipschitz domains
(American Mathematical Society, 1993)
The Martin boundary with respect to the Laplacian and with respect to uniformly elliptic operators in divergence form can be identified with the Euclidean boundary in C [to the power of gamma] domains, where [gamma](x) = bx log log(1/x)/ log log log(1/x), b small. A counterexample shows that this result is very nearly sharp.
The level sets of iterated Brownian motion
We show that the Hausdorff dimension of every level set of iterated Brownian motion is equal to 3/4.
The boundary Harnack principle for non-divergence form elliptic operators
(Cambridge University Press, 1994)
If L is a uniformly elliptic operator in non–divergence form, the boundary Harnack principle for the ratio of positive L–harmonic functions holds in Hölder domains of order [alpha] if [alpha] > 1/2. A counterexample shows that 1/2 is sharp. For Hölder domains of order [alpha] with [alpha is an element of the set] (0, 1], the ...