Now showing items 21-30 of 84
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.
Efficient Markovian couplings: Examples and counterexamples
(Institute of Mathematical Statistics, 2000-05)
In this paper we study the notion of an efficient coupling of Markov processes. Informally, an efficient coupling is one which couples at the maximum possible exponential rate, as given by the spectral gap. This notion is of interest not only for its own sake, but also of growing importance arising from the recent advent ...
Super-Brownian motion with reflecting historical paths
(Springer-Verlag GmbH, 2001-12)
We consider super-Brownian motion whose historical paths reflect from each other, unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions corresponding to a sequence of discrete approximations but we leave the problem of uniqueness of the limit open. We prove a few results ...
On non-increase of Brownian motion
(Institute of Mathematical Statistics, 1990-07)
A new proof of the non-increase of Brownian paths is given.
An asymptotically 4-stable process
(CRC Press, 1995)
An asymptotically 4-stable process is constructed. The model identifies the 4-stable process with a sequence of processes converging in a very weak sense. It is proved that the 4-th variation of the process is a linear function of time and its quadratic variation may be identified with a Brownian motion.
Variation of iterated Brownian motion
(American Mathematical Society, 1994)
In this paper, we study higher order variations of iterated Brownian motion (IBM) with view towards possible applications to the construction of the stochastic integral with respect to IBM. We prove that the 4-th variation of IBM is a deterministic linear function. This clearly means that the quadratic variation is infinite ...
A counterexample to the "hot spots" conjecture
(Princeton University and Institute for Advanced Study, 1999-01)
We construct a counterexample to the "hot spots" conjecture; there exists a bounded connected planar domain (with two holes) such that the second eigenvalue of the Laplacian in that domain with Neumann boundary conditions is simple and such that the corresponding eigenfunction attains its strict maximum at an interior point ...
A boundary Harnack principle in twisted Hölder domains
(Annals of Mathematics, 1991-09)
The boundary Harnack principle for the ratio of positive harmonic functions is shown to hold in twisted Hölder domains of order [alpha] for [alpha is an element of the set](1/2, 1]. For each [alpha is an element of the set] (0, 1/2), there exists a twisted Hölder domain of order [alpha] for which the boundary Harnack principle ...
Excursion laws and exceptional points on Brownian paths
The purpose of this note is to present an example of a family of "exceptional points" on Brownian paths which cannot be constructed using an entrance law.