Discrete Periodic Sampling with Jitter and Almost Periodically Correlated Processes |
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Authors: | Dominique Dehay Vincent Monsan |
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Institution: | 1.IRMAR,Université Rennes,France;2.UFR Sciences Sociales,Université de Rennes 2 Haute-Bretagne,Rennes cedex,France;3.Université de Cocody,Abidjan,C?te d’Ivoire |
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Abstract: | The zero-mean process
is said to be almost periodically correlated whenever its shifted covariance kernel is almost periodic in t uniformly with respect to . Then it admits a Fourier–Bohr decomposition: . This paper deals with the estimation of the spectral covariance a(λ,τ) from a discrete time observation of the process , when jitter and delay phenomena are present in conjunction with periodic sampling. Under mixing conditions, we establish
the consistency and the asymptotic normality of empirical estimators as the sampling time step tends to 0 and the sampling
period tends to infinity.
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Keywords: | Continuous time process Almost periodic covariance Spectral covariance Discrete time sampling Jitter Consistent estimator |
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