Hausdorff Dimension in Stochastic Dispersion

Dimension in Stochastic Dispersion

We consider the evolution of a connected set in Euclidean space carried by a periodic incompressible stochastic flow. While for almost every realization of the random flow at time t most of the particles are at a distance of order √ t away from the origin [DKK1], there is an uncountable set of measure zero of points, which escape to infinity at the linear rate [CSS1]. In this paper we prove tha...

un 2 00 9 Hausdorff dimension and hierarchical system dynamics

We show that Hausdorff dimension may be used to distinguish different dynamics of the relaxation in hierarchical systems. We examine the hierarchical systems following the temperature-dependent power-law decay and the Kohlrausch law. For our purposes, we consider a Lévy stochastic processes on p−adic integer numbers.

Stochastic independence with respect to upper and lower conditional probabilities defined by Hausdorff outer and inner measures

Variational dimension of random sequences and its application

A concept of variational dimension is introduced for a random sequence with stationary increments. In Gaussian case the variational dimension in the limit coincides with the Hausdorff dimension of a proper random process. Applications of the concept are illustrated by examples of neurological data and network traffic analysis.

Historic set carries full hausdorff dimension

‎We prove that the historic set for ratio‎ ‎of Birkhoff average is either empty or full of Hausdorff dimension in a class of one dimensional‎ ‎non-uniformly hyperbolic dynamical systems.