Sojourn time dimensions of fractional Brownian motion

On time-dependent neutral stochastic evolution equations with a fractional Brownian motion and infinite delays

In this paper, we consider a class of time-dependent neutral stochastic evolution equations with the infinite delay and a fractional Brownian motion in a Hilbert space. We establish the existence and uniqueness of mild solutions for these equations under non-Lipschitz conditions with Lipschitz conditions being considered as a special case. An example is provided to illustrate the theory

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

Simulation of fractional Brownian motion

Preface In recent years, there has been great interest in the simulation of long-range dependent processes, in particular fractional Brownian motion. Motivated by applications in communications engineering, I wrote my master's thesis on the subject in 2002. Since many people turned out to be interested in various aspects of fractional Brownian motion, I decided to update my thesis and make it p...

Wavelet Analysis of Fractional Brownian Motion in Multifractal Time

We study fractional Brownian motions in multifractal time, a model for multifractal processes proposed recently in the context of economics. Our interest focuses on the statistical properties of the wavelet decomposition of these processes, such as residual correlations (LRD) and stationarity, which are instrumental towards computing the statistics of wavelet-based estimators of the multifracta...