A fractional Brownian field indexed by $L^2$ and a varying Hurst parameter

As a by-product, geometric rough paths associated to elements of the reproducing kernel Hilbert space of the fractional Brownian motion are obtained and an explicit

Corollary 5.4 Let f be α-H¨ older continuous, i.e. Then the critical order of differen- tiability and the fractional degree of differentiability agree and are equal to the order of

Indeed, for a fBm, a Hurst exponent above (respectively below) 1/2 means persistence (resp. anti-persistence) of the increments. Therefore, in fields as diverse as finance [11, 27,

Key words: frational Brownian motion, Gaussian proesses, H older regu-.. larity, loal asymptoti self-similarity,

the time reversed process is a drifted fractional Brownian motion, which continuously extends the one obtained in the theory of time reversal of Brownian diffusions when H = 1/2..

The aim of this paper is to propose confidence intervals for the Hurst parameter based on a single observation of a discretized sample path of the interval [0, 1] of a

Abstract: 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

Key words: H¨ older continuity, fractional Brownian motion, Skorohod integrals, Gaussian sobolev spaces, rough path, distributions.. AMS Subject classification (2000): 60G15,