51 citations · 84 across the 17 of their papers we have counts for
22 papers
An Optimal Uniform Modulus of Continuity for Harmonizable Fractional Stable Motion
Antoine Ayache, Yimin Xiao
Non-Gaussian Harmonizable Fractional Stable Motion (HFSM) is a natural and important extension of the well-known Fractional Brownian Motion to the framework of heavy-tailed stable…
Asymptotic normality for a modified quadratic variation of the Hermite process
Antoine Ayache, Ciprian A Tudor
We consider a modified quadratic variation of the Hermite process based on some well-chosen increments of this process. These special increments have the very useful property to be…
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…
Asymptotic normality of simultaneous estimators of cyclic long-memory processes
Antoine Ayache, Myriam Fradon, Ravindi Nanayakkara +1
Spectral singularities at non-zero frequencies play an important role in investigating cyclic or seasonal time series. The publication [2] introduced the generalized filtered metho…
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…
Lower bound for local oscillations of Hermite processes
Antoine Ayache
The most known example of a class of non-Gaussian stochastic processes which belongs to the homogenous Wiener chaos of an arbitrary order N > 1 are probably Hermite processes of ra…