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Now showing items 21-30 of 84

#### Percolation dimension of fractals

(Academic Press (Elsevier), 1990-01)

"Percolation dimension" is introduced in this note. It characterizes certain fractals and its definition is based on the Hausdorff dimension. It is shown that percolation dimension and "boundary dimension" are in a sense independent from the Hausdorff dimension and, therefore, provide an additional tool for classification of ...

#### Non-polar points for reflected Brownian motion

(Elsevier, 1993)

Our main results are (i) a new construction of reflected Brownian motion X in a half-plane with non-smooth angle of oblique reflection and
(ii) a theorem on existence of some "exceptional" points on the paths of the standard two-dimensional Brownian motion. The link between these two seemingly disparate results will be formed ...

#### Hitting a boundary point with reflected Brownian motion

(Springer-Verlag, 1992)

An explicit integral test involving the reflection angle is given for the reflected Brownian motion in a half-plane to hit a fixed boundary point.

#### A boundary Harnack principle in twisted Hölder domains

(Annals of Mathematics, 1991-09)

The boundary Harnack principle for the ratio of positive harmonic functions is shown to hold in twisted Hölder domains of order [alpha] for [alpha is an element of the set](1/2, 1]. For each [alpha is an element of the set] (0, 1/2), there exists a twisted Hölder domain of order [alpha] for which the boundary Harnack principle ...

#### Excursion laws and exceptional points on Brownian paths

(Springer-Verlag, 1993)

The purpose of this note is to present an example of a family of "exceptional points" on Brownian paths which cannot be constructed using an entrance law.

#### 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.

#### An asymptotically 4-stable process

(CRC Press, 1995)

An asymptotically 4-stable process is constructed. The model identifies the 4-stable process with a sequence of processes converging in a very weak sense. It is proved that the 4-th variation of the process is a linear function of time and its quadratic variation may be identified with a Brownian motion.

#### Variation of iterated Brownian motion

(American Mathematical Society, 1994)

In this paper, we study higher order variations of iterated Brownian motion (IBM) with view towards possible applications to the construction of the stochastic integral with respect to IBM. We prove that the 4-th variation of IBM is a deterministic linear function. This clearly means that the quadratic variation is infinite ...

#### On non-increase of Brownian motion

(Institute of Mathematical Statistics, 1990-07)

A new proof of the non-increase of Brownian paths is given.

#### 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 ...