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Complete description of all self-similar models driven by Lévy stable noise
A canonical decomposition of H-self-similar Lévy symmetric α-stable processes is
presented. The resulting components completely described by both deterministic kernels …
presented. The resulting components completely described by both deterministic kernels …
On the structure of stationary stable processes
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 …
the ergodic theory of nonsingular flows is established and exploited. Using this connection …
On the structure and representations of max-stable processes
We develop classification results for max-stable processes, based on their spectral
representations. The structure of max-linear isometries and minimal spectral representations …
representations. The structure of max-linear isometries and minimal spectral representations …
[HTML][HTML] Multivariate operator-self-similar random fields
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 …
the time domain and the state space are studied. Such random fields are called operator-self …
Representations and isomorphism identities for infinitely divisible processes
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 …
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 …
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
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 …
processes. Originally, both decompositions were defined in an abstract way based on the …
Approximation of supremum of max-stable stationary processes & Pickands constants
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) …
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
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 …
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
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 …
and α-Fréchet random fields. We show that the result of Samorodnitsky Ann. Probab. 33 …