Statistical test for fractional Brownian motion based on detrending moving average algorithm

Detrending moving average algorithm for multifractals.

The detrending moving average (DMA) algorithm is a widely used technique to quantify the long-term correlations of nonstationary time series and the long-range correlations of fractal surfaces, which contains a parameter θ determining the position of the detrending window. We develop multifractal detrending moving average (MFDMA) algorithms for the analysis of one-dimensional multifractal measu...

An efficient, three-dimensional, anisotropic, fractional Brownian motion and truncated fractional Levy motion simulation algorithm based on successive random additions

Fluid flow and solute transport in the subsurface are known to be strongly influenced by the heterogeneity of aquifers. To simulate aquifer properties, such as logarithmic hydraulic conductivity (lnðKÞ) variations, fractional Brownian motion (fBm) and truncated fractional Levy motion (fLm) were suggested previously. In this paper, an efficient three-dimensional successive random additions (SRA)...

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.

Self-Similar Processes, Fractional Brownian Motion and Statistical Inference

Self-similar stochastic processes are used for stochastic modeling whenever it is expected that long range dependence may be present in the phenomenon under consideration. After discusing some basic concepts of self-similar processes and fractional Brownian motion, we review some recent work on parametric and nonparametric inference for estimation of parameters for linear systems of stochastic ...

Tempered fractional Brownian motion