## Search

Now showing items 1-10 of 36

#### 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 ...

#### Super-Brownian motion with reflecting historical paths

(Springer-Verlag GmbH, 2001-12)

We consider super-Brownian motion whose historical paths reflect from each other, unlike those of the usual historical super-Brownian motion. We prove tightness for the family of distributions corresponding to a sequence of discrete approximations but we leave the problem of uniqueness of the limit open. We prove a few results ...

#### Variably skewed Brownian motion

(Institute of Mathematical Statistics, 2000-03-01)

Given a standard Brownian motion B, we show that the equation X [subscript] t = x [subscript] 0 + B [subscript] t + [beta](L [to the power of X] [subscript] t ); t [is greater than or equal to] 0 ; has a unique strong solution X. Here L [to the power of X] is the symmetric local time of X at 0, and [beta] is a given differentiable ...

#### Fiber Brownian motion and the "hot spots" problem

(Duke University Press, 2000-10)

We show that in some planar domains both extrema of
the second Neumann eigenfunction lie strictly inside the domain. The main technical innovation is the use of "fiber Brownian motion," a process which
switches between two-dimensional and one-dimensional evolution.

#### Local time flow related to skew Brownian motion

(Institute of Mathematical Statistics, 2001-10)

We define a local time flow of skew Brownian motions, i.e., a family of solutions to the stochastic differential equation defining the skew Brownian motion, starting from different points but driven by the same Brownian motion. We prove several results on distributional and path properties of the flow. Our main result is a ...

#### 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 ...

#### 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 ...

#### 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.