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… Expand

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… Expand

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… Expand

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… Expand

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… Expand

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… Expand

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… Expand