Ergodic properties of Poissonian ID processes
By E. Roy. 2007
53 citations recorded by the source corpus.
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 Levy 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.
Subfields: Finance, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/fe8c5c43a3035d547b9429f2e9cdd582de284f8b
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In Finance
- Zakhar Kabluchko
- Martin Schlather
- A. C. Davison
- E. Roy
- Mathieu Ribatet
- Raphaël Huser
- Emeric Thibaud
- Sebastian Engelke
In Mathematical Physics
- Martin Schlather
- Zakhar Kabluchko
- E. Roy
- A. C. Davison
- Sebastian Engelke
- Mathieu Ribatet
- Raphaël Huser
- Emeric Thibaud
Citations in the corpus
- Ergodic properties of max-infinitely divisible processes (2009, background): “A criterion for ergodicity in terms of the spectral representation of the process was established in [22], see also [21].”
- Poisson suspensions and infinite ergodic theory (2008, background): “We recall that these processes are exactly those that can be obtained as stochastic integrals with respect to a Poisson measure (see [13] and [18]).”