Self-similar processes are stochastic processes that are invariant in distribution under
suitable time scaling, and are a subject intensively studied in the last few decades. This …

The fractal or Hausdorff dimension is a measure of roughness (or smoothness) for time
series and spatial data. The graph of a smooth, differentiable surface indexed in ℝ d has …

Quadratic variations and estimation of the local H6lder index of a Gaussian process Page 1
Ann. Inst. Henri Poincare’, Vol. 33, no 4, 1997, p. 407-436. Prohabilith et Stutistiques Quadratic …

Limit distribution results on realized power variation, that is, sums of absolute powers of
increments of a process, are derived for certain types of semimartingale with continuous …

This paper develops a class of consistent estimators of the parameters of a fractional
Brownian motion based on the asymptotic behavior of the k-th absolute moment of discrete …

Fractals everywhere! This is the title of a bestseller, but it is also a reality: Fractals are really
everywhere. What a change since the days of Charles Hermite declaring “I turn away with …

Objectives To examine whether trabecular bone texture (TBT) parameters assessed on
computed radiographs could predict knee osteoarthritis (OA) progression. Methods This …

Using multiple stochastic integrals and the Malliavin calculus, we analyze the asymptotic
behavior of quadratic variations for a specific non-Gaussian self-similar process, the …

The generalized multifractional Brownian motion (GMBM) is a continuous Gaussian process
that extends the classical fractional Brownian motion (FBM) and multifractional Brownian …

We present fixed domain asymptotic results that establish consistent estimates of the
variance and scale parameters for a Gaussian random field with a geometric anisotropic …