## Search

Now showing items 51-60 of 84

#### 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.

#### Coalescence of synchronous couplings

(Springer-Verlag GmbH, 2002-08)

We consider a pair of reflected Brownian motions in a Lipschitz planar domain starting from different points but driven by the same Brownian motion. First we construct such a pair of processes in a certain weak sense, since it is not known whether a strong solution to the Skorohod equation in Lipschitz domains exists. Then ...

#### 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.

#### 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 ...

#### 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.

#### 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] ...

#### 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.

#### 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 ...

#### Iterated law of iterated logarithm

(Institute of Mathematical Statistics, 1995-10)

Suppose [epsilon] [is a member of the set] [0, 1) and let theta [subscipt epsilon] (t) = (1 − [epsilon]) [square root of] (2tln [subscript] 2 t). Let L [to the power of epsilon] [subscript] t denote the amount of local time spent by Brownian motion on the curve [theta subscript epsilon] (s) before time t. If [epsilon] > 0 ...

#### 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.