Fractional Brownian Motions, Fractional Noises and Applications

  title={Fractional Brownian Motions, Fractional Noises and Applications},
  author={Benoit B. Mandelbrot and John W. Van Ness},
  journal={Siam Review},
Characterizing stochastic resonance in a triple cavity
Stochastic resonance in a triple cavity that consists of three units and is subjected to noise, periodic force and vertical constance force is studied, by calculating the spectral amplification η numerically and it is found that the cavity parameters can eliminate or regulate the maximum of η and the noise intensity that induces this maximum.
Vertical Displacements of the Amazon Basin From GRACE and GPS
The extent to which Gravity Recovery and Climate Experiment (GRACE)‐recovered gravity anomalies can improve our understanding of Global Positioning System (GPS)‐measured vertical displacements is
Stochastic processes for anomalous diffusion
Con difusion anomala se hace referencia a procesos de difusion en los cuales el desplazamiento cuadratico medio (MSD) no es una funcion lineal de la variable tiempo (lo que se conoce como difusion
Efficient Simulation of Fluid Flow and Transport in Heterogeneous Media Using Graphics Processing Units (GPUs)
An overall speed-up factor of about one order of magnitude or better is obtained, which increases with the size of the network, and approximate but accurate bounds for the permeability anisotropy for stratified porous media are obtained.
Affine representations of fractional processes with applications in mathematical finance
Degree project Stock-Price Modeling by the Geometric Fractional Brownian Motion
As an extension of the geometric Brownian motion, a geometric fractional Brownian motion (GFBM) is considered as a stock-price model. The modeled GFBM is compared with empirical Chinese stock prices.
Escalonamento de recursos em redes LTE utilizando processo envelope de tráfego multifractal e curva de serviço mínima
Neste trabalho, propoe-se inicialmente uma variacao da modelagem MWM (Multifractal Wavelet Model) para fluxos de trafego de rede, de tal forma que seus parâmetros sejam estimados de maneira
Dynamic Systems and Applications 26 ( 2017 ) 535-548 A FRACTIONAL VERSION OF THE HESTON MODEL WITH HURST PARAMETER H ∈ ( 1 / 2 , 1 )
We consider a fractional version of the Heston model where the two standard Brownian motions are replaced by two fractional Brownian motions with Hurst parameter H ∈ (1/2, 1). We show that the
A Brief History of Long Memory: Hurst, Mandelbrot and the Road to ARFIMA, 1951-1980
The original motivation of the development of long memory and Mandelbrot’s influence on this fascinating field are discussed and the sometimes contrasting approaches to long memory in different scientific communities are elucidated.
Dynamical and collective properties of active and passive particles in Single File
Particles motion inside complex, irregular or crowded environments is a common phenomenon ranging from microscopic to macroscopic scales. It can be involved in everyday practical problems, like


The typical spectral shape of an economic variable
In recent years, a number of power spectra have been estimated from economic data and the majority have been found to be of a similar shape. A number of implications of this shape are discussed,
Statistical theory of turbulenc
  • G. Taylor
  • Geology
    Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences
  • 1935
Since the time of Osborne Reynolds it has been known that turbulence produces virtual mean stresses which are proportional to the coefficient of correlation between the components of turbulent
Random Fourier transforms
Independence and Dependence
A stochastic process is commonily used as a model in studying the behavior of a random system through time. It will be convenient for us to take the stochastic process {xtJ as discrete in time t = *,