## Search

Now showing items 11-20 of 32

#### On non-increase of Brownian motion

(Institute of Mathematical Statistics, 1990-07)

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

#### 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 ...

#### 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.

#### 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? ...

#### Erratum to The Supremum of Brownian Times on Hölder Curves

(Birkhauser, 2002-05-21)

For [function] f [maps the set]: [0, 1] [into the set] [Real numbers], we consider L [superscript] f [subscript] t , the local time of spacetime Brownian motion on the curve f. Let S [subscript][sigma] be the class of all functions whose Hölder norm of order [sigma] is less than or equal to 1. We show that the supremum of L ...

#### The supremum of Brownian local times on Holder curves

(Elsevier, 2001-11)

For f : [maps the set] [0, 1] [into the set of real numbers] R, we consider L ([to the power of] f [subscript] t), the local time of spacetime
Brownian motion on the curve f. Let S [subscript alpha] be the class of all functions whose Holder norm of order [alpha] is less than or equal to 1. We show that the supremum of L ...

#### 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.