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article · The Annals of Probability · 2007

Ergodic properties of Poissonian ID processes

Emmanuel Roy

Cited by 59Open access

Abstract

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.

Cite this paper

APA 7

Roy, E. (2007). Ergodic properties of Poissonian ID processes. The Annals of Probability, 35(2). https://doi.org/10.1214/009117906000000692

MLA 9

Roy, Emmanuel. “Ergodic properties of Poissonian ID processes.” The Annals of Probability, vol. 35, no. 2, 2007, https://doi.org/10.1214/009117906000000692.

Chicago

Roy, Emmanuel. 2007. “Ergodic properties of Poissonian ID processes.” The Annals of Probability 35 (2). https://doi.org/10.1214/009117906000000692.

Harvard

Roy, E. (2007) ‘Ergodic properties of Poissonian ID processes’, The Annals of Probability, 35(2). Available at: https://doi.org/10.1214/009117906000000692.

BibTeX
@article{roy2007ergodic,
  title = {{Ergodic properties of Poissonian ID processes}},
  author = {Roy, Emmanuel},
  journal = {The Annals of Probability},
  volume = {35},
  number = {2},
  year = {2007},
  doi = {10.1214/009117906000000692}
}

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