Characterizing N-dimensional anisotropic Brownian motion by the distribution of diffusivities

Characterizing N-dimensional anisotropic Brownian motion by the distribution of diffusivities.

Anisotropic diffusion processes emerge in various fields such as transport in biological tissue and diffusion in liquid crystals. In such systems, the motion is described by a diffusion tensor. For a proper characterization of processes with more than one diffusion coefficient, an average description by the mean squared displacement is often not sufficient. Hence, in this paper, we use the dist...

The Patched Brownian Motion Distribution

Existence and Measurability of the Solution of the Stochastic Differential Equations Driven by Fractional Brownian Motion

On the Two - Dimensional Fractional Brownian Motion

We study the two-dimensional fractional Brownian motion with Hurst parameter H > 1 2. In particular, we show, using stochastic calculus , that this process admits a skew-product decomposition and deduce from this representation some asymptotic properties of the motion.

Dimensional Properties of Fractional Brownian Motion

Let B = {Bα(t), t ∈ RN} be an (N, d)-fractional Brownian motion with Hurst index α ∈ (0, 1). By applying the strong local nondeterminism of B, we prove certain forms of uniform Hausdorff dimension results for the images of B when N > αd. Our results extend those of Kaufman [7] for one-dimensional Brownian motion. Running head: Dimensional Properties of Fractional Brownian Motion 2000 AMS Classi...