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#### 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? ...

#### 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 ...

#### 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 ...

#### 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.