## 3 Citations

Maxima of stable random fields, nonsingular actions and finitely generated abelian groups: A survey

- Mathematics
- 2017

This is a self-contained introduction to the applications of ergodic theory of nonsingular (also known as quasi-invariant) group actions and the structure theorem for finitely generated abelian…

## References

SHOWING 1-10 OF 36 REFERENCES

Null flows, positive flows and the structure of stationary symmetric stable processes

- Mathematics
- 2004

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…

MINIMAL INTEGRAL REPRESENTATIONS OF STABLE PROCESSES

- Mathematics
- 1998

Abstract: Minimal integral representations are defined for general st ochastic processes and completely characterized for stable processes ( symmetric and asymmetric). In the stable case, minimal…

Stable stationary processes related to cyclic flows

- Mathematics
- 2004

We study stationary stable processes related to periodic and cyclic flows in the sense of Rosinski [Ann. Probab. 23 (1995) 1163–1187]. These processes are not ergodic. We provide their canonical…

Stationary Symmetric α-Stable Discrete Parameter Random Fields

- Mathematics
- 2008

Abstract
We establish a connection between the structure of a stationary symmetric α-stable random field (0<α<2) and ergodic theory of non-singular group actions, elaborating on a previous work by…

The structure of self-similar stable mixed moving averages

- Mathematics
- 2002

Let fi2 (1;2) and Xfi be a symmetric fi-stable (SfiS) process with stationary increments given by the mixed moving average Xfi(t) = Z

Structure of stationary stable processes

- Mathematics
- 1995

A connection between structural studies of stationary non-Gaussian stable processes and the ergodic theory of nonsingular flows is established and exploited. Using this connection, a unique…

On the structure and representations of max-stable processes

- MathematicsAdvances in Applied Probability
- 2010

We develop classification results for max-stable processes, based on their spectral representations. The structure of max-linear isometries and minimal spectral representations play important roles.…

Nonsingular Group Actions and Stationary S alpha S Random Fields

- Mathematics
- 2009

This paper deals with measurable stationary symmetric stable random fields indexed by R^d and their relationship with the ergodic theory of nonsingular R^d-actions. Based on the phenomenal work of…