We consider a passive scalar in a periodic shear flow perturbed by an additive fractional noise with the Hurst exponent H ∈ (0, 1). We establish a diffusive homogenization limit for the tracer when the Hurst exponent H ∈ (0, 1/2). We also identify an intermediate range of times when the tracer behaves diffusively even when H ∈ (1/2, 1). The proof is based on an auxiliary limit theorem for an ad...

Given a two-dimensional fractional multiplicative process (Ft)t∈[0,1] determined by two Hurst exponents H1 and H2, we show that there is an associated uniform Hausdorff dimension result for the images of subsets of [0, 1] by F if and only if H1 = H2.

Explicit formulae for Weber-Schafheitlin’s type integrals with exponent 1 are derived. The results of these integrals are distributions on R+.

While the presence of long-range dependence in the asset returns seems to be a stylized fact, the issue of arguing the possible causes of this phenomena is totally obscure. Trying to shed light in this problem, we investigate the possible sources of the long-range dependence phenomena in the Brazilian Stock Market. For this purpose, we employ a sample which comprises stocks traded in the Brazil...

In this paper, using the atomic theory of the Herz-type Hardy spaces with variable exponent, we give their wavelet characterization by means of some discrete tent spaces with variable exponent at the origin.

The emergence of scaling in transport through interconnected systems is a consequence of the topological structure of the network and the physical mechanisms underlying the transport dynamics. We study transport by advection and diffusion in scale-free and Erdős-Rényi networks. Velocity distributions derived from a flow potential exhibit power-law scaling with exponent ν≈γ+1, where γ is the exp...

Correlated sources are present in communication systems where protocols ensure that there is some predetermined information for sources. Here correlated sources across an eavesdropped channel that incorporate a heterogeneous encoding scheme and their effect on the information leakage when some channel information and a source have been wiretapped is investigated. The information leakage bounds ...