2 citations · 2 across the 7 of their papers we have counts for
10 papers
Numerical simulation of Generalized Hermite Processes
Antoine Ayache, Julien Hamonier, laurent Loosveldt
Hermite processes are paradigmatic examples of stochastic processes which can belong to any Wiener chaos of an arbitrary order; the wellknown fractional Brownian motion belonging t…
Wavelet-Type Expansion of Generalized Hermite Processes with rate of convergence
Antoine Ayache, Julien Hamonier, Laurent Loosveldt
Wavelet-type random series representations of the well-known Fractional Brownian Motion (FBM) and many other related stochastic processes and fields have started to be introduced s…
Wavelet series representation for multifractional multistable Riemann-Liouville process
Antoine Ayache, Julien Hamonier
The main goal of this paper is to construct a wavelet-type random series representation for a random field , defined by a multistable stochastic integral, which generates a mult…
A new Multifractional Process with Random Exponent
Antoine Ayache, Céline Esser, Julien Hamonier
A first type of Multifractional Process with Random Exponent (MPRE) was constructed several years ago in (Ayache, Taqqu, 2005) by replacing in a wavelet series representation of Fr…
Behaviour of linear multifractional stable motion: membership of a critical Hölder space
Antoine Ayache, Julien Hamonier
The study of path behaviour of stochastic processes is a classical topic in probability theory and related areas. In this frame, a natural question one can address is: whether or n…
Uniformly and strongly consistent estimation for the Hurst function of a Linear Multifractional Stable Motion
Antoine Ayache, Julien Hamonier
Since the middle of the 90's, multifractional processes have been introduced for overcoming some limitations of the classical Fractional Brownian Motion model. In their context, th…
Linear Multifractional Stable Motion: representation via Haar basis
Julien Hamonier
The aim of this paper is to give a wavelet series representation of Linear Multifractional Stable Motion (LMSM in brief), which is more explicit than that introduced in (Ayache & H…
Linear Multifractional Stable Motion: wavelet estimation of and $\al$ parameters
Antoine Ayache, Julien Hamonier
Linear Fractional Stable Motion (LFSM) of Hurst parameter and of stability parameter $\al$, is one of the most classical extensions of the well-known Gaussian Fractional Browni…
Linear fractional stable motion: a wavelet estimator of the $\al$ parameter
Antoine Ayache, Julien Hamonier
Linear fractional stable motion, denoted by $\{X_{H,\al}(t)\}_{t\in \R}$, is one of the most classical stable processes; it depends on two parameters and $\al\in (0,2)…
Linear Multifractional Stable Motion: fine path properties
Antoine Ayache, Julien Hamonier
Linear Multifractional Stable Motion (LMSM), denoted by , has been introduced by Stoev and Taqqu in 2004-2005, by substituting to the constant Hurst parameter of a…