Passive advection of fractional Brownian motion by random layered flows

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

Frozen Path Approximation for Turbulent Diffusion and Fractional Brownian Motion in Random Flows

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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...

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