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Periodic and almost periodic flows of periodic Ito equations

C. Tudor — 1992

Mathematica Bohemica

Under the uniform asymptotic stability of a finite dimensional Ito equation with periodic coefficients, the asymptotically almost periodicity of the l p -bounded solution and the existence of a trajectory of an almost periodic flow defined on the space of all probability measures are established.

Wavelet estimation of the long memory parameter for Hermite polynomial of gaussian processes

M. ClauselF. RoueffM. S. TaqquC. Tudor — 2014

ESAIM: Probability and Statistics

We consider stationary processes with long memory which are non-Gaussian and represented as Hermite polynomials of a Gaussian process. We focus on the corresponding wavelet coefficients and study the asymptotic behavior of the sum of their squares since this sum is often used for estimating the long–memory parameter. We show that the limit is not Gaussian but can be expressed using the non-Gaussian Rosenblatt process defined as a Wiener–Itô integral of order 2. This happens even if the original...

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