## Search

Now showing items 31-40 of 84

#### Stable processes have thorns

(Institute of Mathematical Statistics, 2003-01)

Let X(t) be the symmetric [alpha]-stable process in R [to the power of] d, [alpha is an element of the set] (0, 2), d [is greater than or equal to] 2. For f : (0, 1) [approaching] (0,[infinity]) let D(f) be the thorn {x [is an element of the set] R [to the power of] d : x [subscript]1 [is an element of the set] (0, 1), |(x ...

#### 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 ...

#### 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 ...

#### 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? ...

#### Shocks and Business Cycles

(2005)

A popular theory of business cycles is that they are driven by animal spirits: shifts in expectations brought on by sunspots. A prominent example is Howitt and McAfee (AER, 1992). We show that this model has a unique equilibrium if there are payoff shocks of any size. This equilibrium still has the desirable property that ...

#### 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 ...

#### Censored stable processes

(Springer-Verlag GmbH, 2003-09)

We present several constructions of a "censored stable process" in an open set D [is an element of the subset] R [to the power of] n, i.e., a
symmetric stable process which is not allowed to jump outside D. We address the question of whether the process will approach the boundary of D in a finite time—we give sharp conditions ...

#### 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 ...