Open Access
March 2007 Ergodic properties of Poissonian ID processes
Emmanuel Roy
Ann. Probab. 35(2): 551-576 (March 2007). DOI: 10.1214/009117906000000692


We show that a stationary IDp process (i.e., an infinitely divisible stationary process without Gaussian part) can be written as the independent sum of four stationary IDp processes, each of them belonging to a different class characterized by its Lévy measure. The ergodic properties of each class are, respectively, nonergodicity, weak mixing, mixing of all order and Bernoullicity. To obtain these results, we use the representation of an IDp process as an integral with respect to a Poisson measure, which, more generally, has led us to study basic ergodic properties of these objects.


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Emmanuel Roy. "Ergodic properties of Poissonian ID processes." Ann. Probab. 35 (2) 551 - 576, March 2007.


Published: March 2007
First available in Project Euclid: 30 March 2007

zbMATH: 1146.60031
MathSciNet: MR2308588
Digital Object Identifier: 10.1214/009117906000000692

Primary: 37A05 , 60E07 , 60G10
Secondary: 37A40 , 60G55

Keywords: ergodic theory , Infinitely divisible stationary processes , infinite-measure preserving transformations , Poisson suspensions

Rights: Copyright © 2007 Institute of Mathematical Statistics

Vol.35 • No. 2 • March 2007
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