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Now showing items 11-20 of 36

#### 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.

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### 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 ...

#### On nodal lines of Neumann eigenfunctions

(Institute of Mathematical Statistics, 2002-06-03)

We present a new method for locating the nodal line of the second eigenfunction for the Neumann problem in a planar domain.

#### Stochastic differential equations driven by stable processes for which pathwise uniqueness fails

(North-Holland (Elsevier), 2004-05)

Let Z [subscript] t be a one-dimensional symmetric stable process of order [alpha] with [alpha is an element of the set] (0, 2) and consider the stochastic differential equation
dX [subscript] t = [omega] (X [subscript] t−)dZ [subscript]t.
For [beta] < 1 [divided by alpha] ^ 1, we show there exists a function that is ...

#### Coalescence of skew Brownian motions

(Springer-Verlag, 2001)

The purpose of this short note is to prove almost sure coalescence of two skew Brownian motions starting from different initial points, assuming that they are driven by the same Brownian motion. The result is very simple but we would like to record it in print as it has already become the foundation of a research project of ...