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Now showing items 11-20 of 21

#### A probabilistic proof of the boundary Harnack principle

(Birkhauser Boston, Inc., 1990)

The main purpose of this paper is to give a probabilistic proof of Theorem 1.1, one using elementary properties of Brownian motion. We also obtain the fact that the Martin boundary equals the Euclidean boundary as an easy corollary of Theorem 1.1. The boundary Harnack principle may be viewed as a Harnack inequality for ...

#### No triple point of planar Brownian motion is accessible

(Institute of Mathematical Statistics, 1996-01)

We show that the boundary of a connected component of the complement of a planar Brownian path on a fixed time-interval contains almost surely no triple point of this Brownian path.

#### A Skorobod-type lemma and a decomposition of reflected Brownian motion

(Institute of Mathematical Statistics, 1995-04)

We consider two-dimensional reflected Brownian motions in sharp thorns pointed downward with horizontal vectors of reflection. We present a decomposition of the process into a Brownian motion and a process which has bounded variation away from the tip of the thorn. The construction is based on a new Skorohod-type lemma.

#### On the time and direction of stochastic bifurcation

(Elsevier, 1998)

This paper is a mathematical companion to an article introducing a new economics model, by Burdzy, Frankel and Pauzner (1997). The motivation of this paper is applied, but the results may have some mathematical interest in their own right. Our model, i.e., equation (1.1) below, does not seem to be known in literature. Despite ...

#### Positivity of Brownian transition densities

(Electronic Journal of Probability, 1997-09-24)

Let B be a Borel subset of R [to the power of] d and let p(t, x, y) be the transition densities of Brownian motion killed on leaving B. Fix x and y in B. If p(t, x, y) is positive for one t, it is positive for every value of t. Some related results are given.

#### Minimal Fine Derivatives and Brownian Excursions

(Nagoya University, 1990-09)

Let f be an analytic function defined on D [is a subset of] [complex numbers] C. If [the derivative of the function f at the point x] has a limit
when [the set] x [into the set] z [is an element of the set partial derivative] D in the minimal fine topology then the limit will be called a minimal fine derivative. Several ...

#### A critical case for Brownian slow points

(Springer-Verlag GmbH, 1996-01)

Let X [subscript] t be a Brownian motion and let S(c) be the set of reals r [is greather than or equal to] 0 such that |X ([subscript] r+t) − X [subscript] r| [is less than or equal to] c [square root of] t, 0 [is less than or equal to] t [is less than or equal to] h, for some h = h(r) > 0. It is known that S(c) is empty if ...

#### 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 ...

#### 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.

#### 2-D Brownian motion in a system of reflecting barriers: effective diffusivity by a sampling method

(Institute of Physics, 1994-02-07)

We study two-dimensional Brownian motion in an ordered periodic system of linear reflecting barriers using the sampling method and conformal transformations. We calculate the effective diffusivity for the Brownian particle. When the periods are fixed but the length of the barrier goes to zero, the effective diffusivity in ...