The Annals of Probability
- Ann. Probab.
- Volume 35, Number 2 (2007), 551-576.
Ergodic properties of Poissonian ID processes
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.
Ann. Probab., Volume 35, Number 2 (2007), 551-576.
First available in Project Euclid: 30 March 2007
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60G10: Stationary processes 60E07: Infinitely divisible distributions; stable distributions 37A05: Measure-preserving transformations
Secondary: 37A40: Nonsingular (and infinite-measure preserving) transformations 60G55: Point processes
Roy, Emmanuel. Ergodic properties of Poissonian ID processes. Ann. Probab. 35 (2007), no. 2, 551--576. doi:10.1214/009117906000000692. https://projecteuclid.org/euclid.aop/1175287754