Sur la convergence uniforme presque complète dans l'estimation de la densité spectrale d'un processus à temps continu après échantillonnage du temps
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Let X={X(t)}t
R be a continuous-time strictly stationary and strongly mixing process. In this paper, we prove in the setting of spectral density estimation, at first, under some hard conditions on the spectral density φX (because of aliasing phenomenon), the uniformly complete convergence of the spectral density estimate from periodic sampling. Afterwards, to overcome aliasing, we consider the sampled process {X(tn)}nZ, where {tn} is a stationary point process independent from X. The uniform complete convergence of the spectral estimate based on the discrete time observations {X(tk),tk} is also obtained. The convergence rates are also established. To cite this article: M. Rachdi, C. R. Acad. Sci. Paris, Ser. I 337 (2003).
R be a continuous-time strictly stationary and strongly mixing process. In this paper, we prove in the setting of spectral density estimation, at first, under some hard conditions on the spectral density φX (because of aliasing phenomenon), the uniformly complete convergence of the spectral density estimate from periodic sampling. Afterwards, to overcome aliasing, we consider the sampled process {X(tn)}nZ, where {tn} is a stationary point process independent from X. The uniform complete convergence of the spectral estimate based on the discrete time observations {X(tk),tk} is also obtained. The convergence rates are also established. To cite this article: M. Rachdi, C. R. Acad. Sci. Paris, Ser. I 337 (2003).