## Search

Now showing items 21-30 of 44

#### On non-increase of Brownian motion

(Institute of Mathematical Statistics, 1990-07)

A new proof of the non-increase of Brownian paths is given.

#### Weak convergence of reflecting Brownian motions

(Institute of Mathematical Statistics, 1998-05-23)

We will show that if a sequence of domains D [subscript] k increases to a domain D then the reflected Brownian motions in D [subscript] k's converge to the reflected Brownian motion in D, under mild technical assumptions. Our theorem follows easily from known results and is perhaps known as a "folk law" among the specialists ...

#### Non-intersection exponents for Brownian paths. Part II: Estimations and applications to a random fractal.

(Institute of Mathematical Statistics, 1990-07)

Let X and Y be independent two-dimensional Brownian motions, X(0) = (0; 0); Y(0) = ([epsilon]; 0), and let p([epsilon]) = P(X[0; 1] [intersected with] Y [0; 1] = [empty set], q([epsilon]) = {Y [0; 1] does not contain a closed loop around 0}. Asymptotic estimates (when [epsilon] --> 0) of p([epsilon]); q([epsilon]),
and some ...

#### Sets avoided by Brownian motion

(Institute of Mathematical Statistics, 1998-04)

A fixed two-dimensional projection of a three-dimensional Brownian motion is almost surely neighborhood recurrent; is this simultaneously true of all the two-dimensional projections with probability one? Equivalently: three-dimensional Brownian motion hits any infinite cylinder with probability one; does it hit all cylinders? ...

#### Configurational transition in a Fleming-Viot-type model and probabilistic interpretation of Laplacian eigenfunctions

(Institute of Physics, 1996-06-07)

We analyze and simulate a two-dimensional Brownian multi-type particle system with death and branching (birth) depending on the position of particles of different types. The system is confined in the two-dimensional box, whose boundaries act as the sink of Brownian particles. The branching rate matches the death rate so that ...

#### A probabilistic proof of the boundary Harnack principle

(Birkhauser Boston, Inc., 1990)

The main purpose of this paper is to give a probabilistic proof of Theorem 1.1, one using elementary properties of Brownian motion. We also obtain the fact that the Martin boundary equals the Euclidean boundary as an easy corollary of Theorem 1.1. The boundary Harnack principle may be viewed as a Harnack inequality for ...

#### No triple point of planar Brownian motion is accessible

(Institute of Mathematical Statistics, 1996-01)

We show that the boundary of a connected component of the complement of a planar Brownian path on a fixed time-interval contains almost surely no triple point of this Brownian path.

#### A Skorobod-type lemma and a decomposition of reflected Brownian motion

(Institute of Mathematical Statistics, 1995-04)

We consider two-dimensional reflected Brownian motions in sharp thorns pointed downward with horizontal vectors of reflection. We present a decomposition of the process into a Brownian motion and a process which has bounded variation away from the tip of the thorn. The construction is based on a new Skorohod-type lemma.

#### Brownian motion in a Brownian crack

(Institute of Mathematical Statistics, 1998-08)

Let D be the Wiener sausage of width [epsilon] around two-sided Brownian motion. The components of two-dimensional reflected Brownian motion in D converge to one-dimensional Brownian motion and iterated Brownian motion, resp., as [epsilon] goes to 0.

#### On the time and direction of stochastic bifurcation

(Elsevier, 1998)

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 ...