We prove finite speed of propagation for stochastic porous media equations perturbed by linear multiplicative space-time rough signals. Explicit and optimal estimates for the speed of propagation are given. The result applies to any continuous driving signal, thus including fractional Brownian motion for all Hurst parameters. The explicit estimates are then used to prove that the corresponding ...

The authors use dynamical analyses to investigate the relation between students’ patterns of interactions with various types of game-based features and their daily performance. High school students (n=40) interacted with a game-based intelligent tutoring system across eight sessions. Hurst exponents were calculated based on students’ choice of interactions with four types of gamebased features:...

Long range dependence induced by heavy tails is a widely reported feature of internet traffic. Long range dependence can be defined as the regular variation of the variance of the integrated process, and half the index of regular variation is then refered to as the Hurst index. The infinite source Poisson process (a particular case of which is the M/G/∞ queue) is a simple and popular model with...

The aim of this paper is to study the d-dimensional stochastic heat equation with a multiplicative Gaussian noise which is white in space and it has the covariance of a fractional Brownian motion with Hurst parameter H ∈ (0, 1) in time. Two types of equations are considered. First we consider the equation in the Itô-Skorohod sense, and later in the Stratonovich sense. An explicit chaos developm...

In this short note, we show how to use concentration inequalities in order to build exact confidence intervals for the Hurst parameter associated with a one-dimensional fractional Brownian motion.

A closed-form expression for shear band spacing in strain-hardening, strain-rate-hardening and thermally softening thermoviscoplastic materials is derived by studying the stability of a homogeneous solution of equations governing its simple shearing deformations. The wavelength of the perturbation that maximizes its initial growth rate is assumed to determine the shear band spacing, Ls: The dep...

It is shown that the law of an SDE driven by fractional Brownian motion with Hurst parameter greater than 1/2 has a smooth density with respect to Lebesgue measure, provided that the driving vector fields satisfy Hörmander’s condition. The main new ingredient of the proof is an extension of Norris’ lemma to this situation.

We present a modelling framework and a fitting method for modelling second order self-similar behaviour with the Markovian Arrival Process (MAP). The fitting method is based on fitting to the autocorrelation function of counts for a second order selfsimilar process. It i s shown that with this fitting algorithm at is possible closely to match the autocorrelation function of counts for a second ...

In this paper, we show how concentration inequalities for Gaussian quadratic form can be used to propose exact confidence intervals of the Hurst index parametrizing a fractional Brownian motion. Both cases where the scaling parameter of the fractional Brownian motion is known or unknown are investigated. These intervals are obtained by observing a single discretized sample path of a fractional ...

Fractal surfaces (’patchwork quilts’) are shown to arise under most general circumstances involving simple bitwise operations between real numbers. A theory is presented for all bitwise operations on a finite alphabet which are not governed by chance. It is shown that these models give rise to a roughness exponent H that shapes the resulting spatial patterns, larger values of the exponent leadi...