Null flows, positive flows and the structure of stationary symmetric stable processes
By Gennady Samorodnitsky. 2004
58 citations recorded by the source corpus.
This paper elucidates the connection between stationary symmetric α-stable processes with 0 < α < 2 and nonsingular flows on measure spaces by describing a new and unique decomposition of stationary stable processes into those corresponding to positive flows and those corresponding to null flows. We show that necessary and sufficient for a stationary stable process to be ergodic is that its positive component vanishes.
Subfields: Finance, Mathematical Physics, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/47b0d688cd04957b527b8b964fe0762f109491e1
How researchers see this paper
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In Finance
- Zakhar Kabluchko
- Yizao Wang
- Stilian A. Stoev
- E. Roy
- Sebastian Engelke
- A. C. Davison
- Mathieu Ribatet
- Martin Schlather
In Mathematical Physics
- Stilian A. Stoev
- Yizao Wang
- Zakhar Kabluchko
- E. Roy
- Martin Schlather
- A. C. Davison
- Sebastian Engelke
- Mathieu Ribatet
In Statistics and Probability
Citations in the corpus
- Spectral representations of sum- and max-stable processes (2009, methodology): “In Theorem 5.1 below we prove a max-stable counterpart of the result of Samorodnitsky (2005).”
- On the structure and representations of max-stable processes (2009, background): “1 of Samorodnitsky [30] about symmetric α-stable processes applies mutatis mutandis to the max-stable case.”
- Ergodic properties of max-infinitely divisible processes (2009, unknown): “41 96 v1 [ m at h. PR ] 2 Keywords : Max–infinitely divisible processes, max–stable processes, ergodicity, mixing, codifference AMS 2000 Subject Classification: Primary, 60G70; Secondary, 60G10”
- Ergodic properties of Poissonian ID processes (2007, methodology): “We can thus replace in this context the previously obtained factorization of Rosiński [13], as well as the refinements of Pipiras and Taqqu [12] and Samorodnitsky [18].”