On the Two - Dimensional Fractional Brownian Motion

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

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

Effects of Brownian motion and Thermophoresis on MHD Mixed Convection Stagnation-point Flow of a Nanofluid Toward a Stretching Vertical Sheet in Porous Medium

This article deals with the study of the two-dimensional mixed convection magnetohydrodynamic (MHD) boundary layer of stagnation-point flow over a stretching vertical plate in porous medium filled with a nanofluid. The model used for the nanofluid incorporates the effects of Brownian motion and thermophoresis in the presence of thermal radiation. The skin-friction coefficient, Nusselt number an...

On two-dimensional fractional Brownian motion and fractional Brownian random field.

As a generalization of one-dimensional fractional Brownian motion (1dfBm), we introduce a class of two-dimensional, self-similar, strongly correlated random walks whose variance scales with power law N(2) (H) (0 < H < 1). We report analytical results on the statistical size and shape, and segment distribution of its trajectory in the limit of large N. The relevance of these results to polymer t...

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...