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math.PR2023
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…
math.PR2023
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…
math.PR2023
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…