Passive scalar motion in a family of random Gaussian velocity fields with longrange correlations is shown to converge to persistent fractional Brownian motions in long times.

The paper obtains the general form of the cross-covariance function of vector fractional Brownian motion with correlated components having different self-similarity indices.

Integration with respect to a fractional Brownian motion with Hurst parameter 1/2 < H < 1 is related to the inner product: (f, g)H = H(2H − 1) ∫

Long-range dependence-Scaling phenomena-(Multi)fractal-Wavelet analysis Scaling analysis-Scaling parameters estimation-Robustness-Fractional Brownian motion synthesis-Fano factor-Aggregation procedure-Allan variance.

Let B(t), t ∈ [−1, 1], be the fractional Brownian motion with Hurst parameter H ∈ ( 1 2 , 1 ) . In this paper we present the series representation

Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy tailed jumps, and the time-fractional version codes heavy tailed waiting times. This paper develops scaling limits and governing equations in the case of correl...

Continuous time random walks impose a random waiting time before each particle jump. Scaling limits of heavy-tailed continuous time random walks are governed by fractional evolution equations. Space-fractional derivatives describe heavy-tailed jumps, and the time-fractional version codes heavy-tailedwaiting times. This paper develops scaling limits and governing equations in the case of correla...

Stochastic di erential games are considered in a non-Markovian setting. Typically, in stochastic di erential games the modulating process of the di usion equation describing the state ow is taken to be Markovian. Then Nash equilibria or other types of solution such as Pareto equilibria are constructed using Hamilton-Jacobi-Bellman (HJB) equations. But in a non-Markovian setting the HJB method i...