Fractional calculus is a rapidly growing field of research, at the interface between probability,
differential equations, and mathematical physics. It is used to model anomalous diffusion, in …

Long-memory, or more generally fractal, processes are known to play an important role in
many scientific disciplines and applied fields such as physics, geophysics, hydrology …

The classical Fickian model for solute transport in porous media cannot correctly predict the
spreading (the dispersion) of contaminant plumes in a heterogeneous subsurface unless its …

Fractional derivatives can be viewed either as handy extensions of classical calculus or,
more deeply, as mathematical operators defined by natural phenomena. This follows the …

Anisotropic Gaussian random fields arise in probability theory and in various applications.
Typical examples are fractional Brownian sheets, operator-scaling Gaussian fields with …

A scalar valued random field [Formula: see text] is called operator-scaling if for some d× d
matrix E with positive real parts of the eigenvalues and some H> 0 we have where= fd …

Abstract Let BH, K={BH, K (t), t∈ ℝ+} be a bifractional Brownian motion in ℝ d. We prove that
BH, K is strongly locally non-deterministic. Applying this property and a stochastic integral …

Abstract Let BH={BH (t), t∈ ℝ N} be an (N, d)-fractional Brownian sheet with index H=(H 1,...,
HN)∈(0, 1) N. The uniform and local asymptotic properties of BH are proved by using …

Sufficient conditions for a real-valued Gaussian random field X={X (t), t∈ RN} with stationary
increments to be strongly locally nondeterministic are proven. As applications, small ball …

This paper is concerned with sample path properties of anisotropic Gaussian random fields.
We establish Fernique-type inequalities and utilize them to study the global and local moduli …