Complete description of all self-similar models driven by Lévy stable noise

A Weron, K Burnecki, S Mercik, K Weron - Physical Review E—Statistical …, 2005‏ - APS
A canonical decomposition of H-self-similar Lévy symmetric α-stable processes is
presented. The resulting components completely described by both deterministic kernels …

On the structure of stationary stable processes

J Rosinski - The Annals of Probability, 1995‏ - JSTOR
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 …

On the structure and representations of max-stable processes

Y Wang, SA Stoev - Advances in Applied Probability, 2010‏ - cambridge.org
We develop classification results for max-stable processes, based on their spectral
representations. The structure of max-linear isometries and minimal spectral representations …

[HTML][HTML] Multivariate operator-self-similar random fields

Y Li, Y **ao - Stochastic Processes and their Applications, 2011‏ - Elsevier
Multivariate random fields whose distributions are invariant under operator-scalings in both
the time domain and the state space are studied. Such random fields are called operator-self …

Representations and isomorphism identities for infinitely divisible processes

J Rosińki - The Annals of Probability, 2018‏ - JSTOR
We propose isomorphism-type identities for nonlinear functionals of general infinitely
divisible processes. Such identities can be viewed as an analogy of the Cameron–Martin …

Ergodic properties of Poissonian ID processes

E Roy - 2007‏ - projecteuclid.org
We show that a stationary IDp process (ie, an infinitely divisible stationary process without
Gaussian part) can be written as the independent sum of four stationary IDp processes, each …

[HTML][HTML] Ergodic decompositions of stationary max-stable processes in terms of their spectral functions

C Dombry, Z Kabluchko - Stochastic Processes and their Applications, 2017‏ - Elsevier
We revisit conservative/dissipative and positive/null decompositions of stationary max-stable
processes. Originally, both decompositions were defined in an abstract way based on the …

Approximation of supremum of max-stable stationary processes & Pickands constants

K Dȩbicki, E Hashorva - Journal of Theoretical Probability, 2020‏ - Springer
Let X (t), t ∈ RX (t), t∈ R be a stochastically continuous stationary max-stable process with
Fréchet marginals Φ _ α, α> 0 Φ α, α> 0 and set M_X (T)=\sup _ t ∈ 0, TX (t), T> 0 MX (T) …

Stationary Symmetric α-Stable Discrete Parameter Random Fields

P Roy, G Samorodnitsky - Journal of Theoretical Probability, 2008‏ - Springer
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 …

Ergodic properties of sum-and max-stable stationary random fields via null and positive group actions

Y Wang, P Roy, SA Stoev - 2013‏ - projecteuclid.org
We establish characterization results for the ergodicity of stationary symmetric α-stable (SαS)
and α-Fréchet random fields. We show that the result of Samorodnitsky Ann. Probab. 33 …