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Interpretation of Continuous-Time Autoregressive Processes as Random Exponential Splines

J. Fageot, J.P. Ward, M. Unser

Proceedings of the Eleventh International Workshop on Sampling Theory and Applications (SampTA'15), Washington DC, USA, May 25-29, 2015, pp. 231–235.


We consider the class of continuous-time autoregressive (CAR) processes driven by (possibly non-Gaussian) Lévy white noises. When the excitation is an impulsive noise, also known as compound Poisson noise, the associated CAR process is a random non-uniform exponential spline. Therefore, Poisson-type processes are relatively easy to understand in the sense that they have a finite rate of innovation. We show in this paper that any CAR process is the limit in distribution of a sequence of CAR processes driven by impulsive noises. Hence, we provide a new interpretation of general CAR processes as limits of random exponential splines. We illustrate our result with simulations.

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AUTHOR="Fageot, J. and Ward, J.P. and Unser, M.",
TITLE="Interpretation of Continuous-Time Autoregressive Processes as
	Random Exponential Splines",
BOOKTITLE="Proceedings of the Eleventh International Workshop on
	Sampling Theory and Applications ({SampTA'15})",
YEAR="2015",
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pages="231--235",
address="Washington DC, USA",
month="May 25-29,",
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