## Search

Now showing items 11-20 of 84

#### Shy Couplings

(2005)

A pair (X; Y) of Markov processes is called a Markov coupling if X and Y have the same transition probabilities and (X;Y) is a Markov process. We say that a coupling is "shy" if there exists a (random) [Epsilon] > 0 such that dist(X [subscript] t; Y [subscript] t) > [Epsilon] for all t [is greater than or equal to] 0. We ...

#### Traps for Reflected Brownian Motion

(Springer-Verlag GmbH, 2005-08-16)

Consider an open set D [is an element of the set] R [The set of Real Numbers] [superscript]d, d [is greater than or equal to] 2, and a closed ball B [is a proper subset of] D. Let E[superscript]xT[subscript]B denote the expectation of the hitting time of B for reflected Brownian motion in D starting from x [is an element of ...

#### The Heat Equation and Reflected Brownian Motion in Time-Dependent Domains

(Institute of Mathematical Statistics, 2004-01)

The paper is concerned with reflecting Brownian motion (RBM) in domains with deterministic moving boundaries, also known as "non-cylindrical domains," and its connections with partial differential equations. Construction is given for reflecting Brownian motion in C3-smooth time-dependent domains in the n-dimensional Euclidean ...

#### The "hot spots" problem in planar domains with one hole.

(Duke University Press, 2005)

There exists a planar domain with piecewise smooth boundary and one hole such that the second eigenfunction for the Laplacian with Neumann boundary conditions attains its maximum and minimum inside the domain.

#### An annihilating-branching particle model for the heat equation with average temperature zero

(2005)

We consider two species of particles performing random walks in a domain in [Real numbers] [superscript] d with reflecting boundary conditions, which annihilate on contact. In addition there is a conservation law so that the total number of particles of each type is preserved: When the two particles of different species ...

#### Comparison of potential theoretic properties of rough domains

(2005)

We discuss the relationships between the notion of intrinsic ultracontractivity, parabolic Harnack principle, compactness of the 1-resolvent of the Neumann Laplacian, and non-trap property for Euclidean domains with finite Lebesgue measure. In particular, we give an answer to an open problem raised by Davies and Simon in 1984 ...

#### Synchronous couplings of reflected Brownian motions in smooth domains

(2005)

For every bounded planar domain D with a smooth boundary, we define a "Lyapunov exponent" [Lambda](D) using a fairly explicit formula. We consider two reflected Brownian motions in D, driven by the same Brownian motion (i.e., a "synchronous coupling"). If [Lambda] (D) > 0 then the distance between the two Brownian particles ...

#### Stochastic bifurcation models

(Institute of Mathematical Statistics, 1999-01)

We study an ordinary differential equation controlled by a stochastic process. We present results on existence and uniqueness of solutions, on associated local times (Trotter and Ray-Knight theorems), and on time and direction of bifurcation. A relationship with Lipschitz approximations to Brownian paths is also discussed.

#### Reduction of dimensionality in a diffusion search process and kinetics of gene expression

(North-Holland (Elsevier), 2000-03-01)

In order to activate a gene in a DNA molecule a specific protein (transcription factor) has to
bind to the promoter of the gene. We formulate and partially answer the following question: how much time does a transcription factor, which activates a given gene, need in order to find this gene inside the nucleus of a cell? The ...

#### 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 ...