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Now showing items 61-70 of 84

#### 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 ...

#### 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 ...

#### Uniqueness for reflecting Brownian motion in lip domains

(Elsevier, 2005-03)

A lip domain is a Lipschitz domain where the Lipschitz constant is strictly less than one. We prove strong existence and pathwise uniqueness for the solution X = {X [subscript] t, t [is less than or equal to] 0} to the Skorokhod equation dX [subscript] t = dW [subscript] t + n(X [subscript] t)dL [subscript] t, in planar lip ...

#### Ito formula for an asymptotically 4-stable process

(Institute of Mathematical Statistics, 1996-02)

An Ito-type formula is given for an asymptotically 4-stable process.

#### Eigenvalue expansions for Brownian motion with an application to occupation times

(Institute of Mathematical Statistics, 1996-01-31)

Let B be a Borel subset of R [to the power of] d with finite volume. We give an eigenvalue expansion for the transition densities of Brownian motion killed on exiting B. Let A [subscript] 1 be the time spent by Brownian motion in a closed cone with vertex 0 until time one. We show that lim [subscript] u [approaching] 0 log P ...

#### 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.

#### Fast equilibrium selection by rational players living in a changing world

(The Econometric Society, 2001-01)

We study a coordination game with randomly changing payoffs and small frictions in changing actions. Using only backwards induction, we find that players must coordinate on the risk-dominant equilibrium. More precisely, a continuum of fully rational players are randomly matched to play a symmetric 2 x 2 game. The payoff matrix ...

#### Lenses in skew Brownian flow

(Institute of Mathematical Statistics, 2004-10)

We consider a stochastic flow in which individual particles follow skew Brownian motions, with each one of these processes driven by the same Brownian motion. One does not have uniqueness for the solutions of the corresponding stochastic differential equation simultaneously for all real initial conditions. Due to this lack ...

#### Super-Brownian motion with reflecting historical paths. II: Convergence of approximations

(Springer-Verlag GmbH, 2005-10)

We prove that the sequence of finite reflecting branching Brownian motion forests defined by Burdzy and Le Gall ([?]) converges in probability to the "super-Brownian motion with reflecting historical paths." This solves an open problem posed in [?], where only tightness was proved for the sequence of approximations. Several ...