Hurst exponents, Markov processes, and fractional Brownian motion

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 ...

Hurst parameter estimation on fractional Brownian motion and its application to the development of the zebrafish

In order to distinguish different morphogenic fields automatically, fractional Brownian motion is used in this paper and the Hurst parameter is used as an important measure to distinguish different morphogenic fields in embryo of zebra fish.

Hurst exponent estimation of Fractional Lévy Motion

In this paper, we build an estimator of the Hurst exponent of a fractional Lévy motion. The stochastic process is observed with random noise errors in the following framework: continuous time and discrete observation times. In both cases, we prove consistency of our wavelet type estimator. Moreover we perform some simulations in order to study numerically the asymptotic behaviour of this estimate.

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