Dimensional Properties of Fractional Brownian 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...

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.

Lacunary Fractional Brownian Motion

In this paper, a new class of Gaussian field is introduced called Lacunary Fractional Brownian Motion. Surprisingly we show that usually their tangent fields are not unique at every point. We also investigate the smoothness of the sample paths of Lacunary Fractional Brownian Motion using wavelet analysis.

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...

Tempered fractional Brownian motion