ASYMPTOTIC PROPERTY OF SPECTRAL DENSITY ESTIMATORS OF A CONTINUOUS TIME PROCESS ALMOST PERIODICALLY CORRELATED LOW DEPENDENT BY POISSON

2021 ◽  
pp. 145-189
Author(s):  
Sylvestre Placide Ekra ◽  
Vincent Monsan
Keyword(s):  
Spectral Density ◽  
Asymptotic Property ◽  
Continuous Time ◽  
Time Process ◽  
Continuous Time Process ◽  
Density Estimators

scholarly journals Mixed Spectra for Stable Signals from Discrete Observations

2021 ◽  
Vol 12 (05) ◽  
pp. 21-44
Author(s):  
Rachid Sabre
Keyword(s):  
Spectral Density ◽  
Continuous Time ◽  
Continuous Measurement ◽  
Spectral Measurement ◽  
Polynomial Kernel ◽  
Time Process ◽  
Discrete Observations ◽  
Continuous Part ◽  
Continuous Time Process ◽  
Discrete Measurement

This paper concerns the continuous-time stable alpha symmetric processes which are inivitable in the modeling of certain signals with indefinitely increasing variance. Particularly the case where the spectral measurement is mixed: sum of a continuous measurement and a discrete measurement. Our goal is to estimate the spectral density of the continuous part by observing the signal in a discrete way. For that, we propose a method which consists in sampling the signal at periodic instants. We use Jackson's polynomial kernel to build a periodogram which we then smooth by two spectral windows taking into account the width of the interval where the spectral density is non-zero. Thus, we bypass the phenomenon of aliasing often encountered in the case of estimation from discrete observations of a continuous time process.

Stochastic ordering of random processes with an imbedded point process

1991 ◽  
Vol 28 (3) ◽  
pp. 553-567 ◽  
Author(s):  
François Baccelli
Keyword(s):  
Point Process ◽  
Continuous Time ◽  
Random Sequence ◽  
Stochastic Ordering ◽  
Random Processes ◽  
Time Process ◽  
Continuous Time Process ◽  
Partial Orderings ◽  
Stationary Probabilities

We introduce multivariate partial orderings related with the Palm and time-stationary probabilities of a point process. Using these orderings, we give conditions for the monotonicity of a random sequence, with respect to some integral stochastic ordering, to be inherited with a continuous time process in which this sequence is imbedded. This type of inheritance is also discussed for the property of association.

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