Fractional Brownian Motion with Variable Hurst Parameter: Definition and Properties

The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6

Let B be a fractional Brownian motion with Hurst parameter H = 1/6. It is known that the symmetric Stratonovich-style Riemann sums for ∫ g(B(s)) dB(s) do not, in general, converge in probability. We show, however, that they do converge in law in the Skorohod space of càdlàg functions. Moreover, we show that the resulting stochastic integral satisfies a change of variable formula with a correcti...

Definition, properties and wavelet analysis of multiscale fractional Brownian motion

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.

Exact confidence intervals for the Hurst parameter of a fractional Brownian motion

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.

Confidence intervals for the Hurst parameter of a fractional Brownian motion based on finite sample size

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 ...