38 Citations
Ergodic decompositions of stationary max-stable processes in terms of their spectral functions
- Mathematics
- 2016
Random tessellations associated with max-stable random fields
- Mathematics
- 2014
With any max-stable random process $\eta$ on $\mathcal{X}=\mathbb{Z}^d$ or $\mathbb{R}^d$, we associate a random tessellation of the parameter space $\mathcal{X}$. The construction relies on the…
Phase transition for extremes of a family of stationary multiple-stable processes
- Mathematics
- 2021
We investigate a family of stationary processes that may exhibit either long-range or short-range dependence, depending on the parameters. The processes can be represented as multiple stable…
Tail Probability of the Supremum of a Random Walk with Stable Steps and a Nonlinear Negative Drift
- Mathematics
- 2013
We study the tail behavior of the supremum of a random walk with stationary ergodic stable increments and a negative drift. In actuarial mathematics, this gives the ruin probability under a…
Maharam extension and stationary stable processes
- Mathematics
- 2012
We give a second look at stationary stable processes by interpreting the self-similar property at the level of the Levy measure as characteristic of a Maharam system. This allows us to derive…
Growth rates of sample covariances of stationary symmetric α-stable processes associated with null recurrent Markov chains
- Mathematics
- 2000
Symmetric Stable Processes on Amenable Groups
- Mathematics
- 2022
We show that if G is a countable amenable group, then every stationary non-Gaussian symmetric stable ( SαS ) process indexed by G is ergodic if and only if it is weakly-mixing, and it is ergodic if…
References
SHOWING 1-10 OF 17 REFERENCES
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…
Stable mixed moving averages
- Mathematics
- 1993
SummaryThe class of (non-Gaussian) stable moving average processes is extended by introducing an appropriate joint randomization of the filter function and of the stable noise, leading to stable…