Fractional Brownian motion satisfies two-way crossing

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.

Tempered fractional Brownian motion

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...

Fractional Brownian motion and data

We analyze the fractal behavior of the high frequency part of the Fourier spectrum of fBm using multifractal analysis and show that it is not consistent with what is measured on real traac traces. We propose two extensions of fBm which come closer to actual traac traces multifractal properties.