## Search

Now showing items 61-70 of 84

#### 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 ...

#### Conditioned Brownian motion in planar domains

(Springer-Verlag GmbH, 1995-04)

We give an upper bound for the Green functions of conditioned Brownian motion in planar domains. A corollary is the conditional gauge theorem in bounded planar domains.

#### 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.

#### Mechanisms for facilitated target location and the optimal number of molecules in the diffusion search process

(American Physical Society, 2001-06-26)

We investigate the number N of molecules needed to perform independent diffusions in order to achieve bonding of a single molecule to a specific site in time t [subscript] 0. For a certain range of values of t [subscript] 0, an increase from N to k · N molecules (k > 1) results in the decrease of search time from t [subscript] ...

#### 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 ...

#### On domain monotonicity of the Neumann heat kernel

(Academic Press (Elsevier), 1993-08-15)

Some examples are given of convex domains for which domain monotonicity of the Neumann heat kernel does not hold.

#### Geometric Properties of 2-dimensional Brownian Paths

(Springer-Verlag GmbH, 1989)

Let A be the set of all points of the plane C, visited by two-dimensional Brownian motion before time 1. With probability 1, all points of A are "twist points" except a set of harmonic measure zero. "Twist points" may be continuously approached in [the set that contains all those elements of complex numbers that are not in] ...

#### Labyrinth dimension of Brownian trace

(Institute of Mathematics, 1995)

Suppose that X is a two-dimensional Brownian motion. The trace X[0, 1] contains a self-avoiding continuous path whose Hausdorff dimension is equal to 2.

#### 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 ...

#### Some path properties of iterated Brownian motion

(Birkhauser Boston, Inc., 1993)

The present paper is devoted to studying path properties of iterated Brownian motion (IBM). We want to examine how the lack of independence of increments influences the results and estimates which are well understood in the Brownian case. This may be viewed as a prelude to a deeper study of the process.