On the structure and representations of max-stable processes

@article{Wang2010OnTS,
  title={On the structure and representations of max-stable processes},
  author={Yizao Wang and Stilian A. Stoev},
  journal={Advances in Applied Probability},
  year={2010},
  volume={42},
  pages={855 - 877}
}
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. We propose a general classification strategy for measurable max-stable processes based on the notion of co-spectral functions. In particular, we discuss the spectrally continuous-discrete, the conservative-dissipative, and the positive-null decompositions. For stationary max-stable processes, the… 
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References

SHOWING 1-10 OF 55 REFERENCES
Spectral representations of sum- and max-stable processes
To each max-stable process with α-Fréchet margins, α ∈ (0,2), a symmetric α-stable process can be associated in a natural way. Using this correspondence, we deduce known and new results on spectral
Stable stationary processes related to cyclic flows
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
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, a unique
Null flows, positive flows and the structure of stationary symmetric stable processes
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
Decomposition of stationary $\alpha$-stable random fields
TLDR
It is shown that every stationary a-stable random field can be uniquely decomposed into the sum of three independent components belonging to these classes.
On uniqueness of the spectral representation of stable processes
In this paper we show that any two spectral representations of a symmetric stable process may differ only by a change of variable and a parameter-independent multiplier. Our result can immediately be
Stationary min-stable stochastic processes
We consider the class of stationary stochastic processes whose margins are jointly min-stable. We show how the scalar elements can be generated by a single realization of a standard homogeneous
Stationary max-stable fields associated to negative definite functions.
Let Wi, i∈ℕ, be independent copies of a zero-mean Gaussian process {W(t), t∈ℝd} with stationary increments and variance σ2(t). Independently of Wi, let ∑i=1∞δUi be a Poisson point process on the real
Max-infinitely divisible and max-stable sample continuous processes
SummaryConditions for a process ζ on a compact metric spaceS to be simultaneously max-infinitely divisible and sample continuous are obtained. Although they fall short of a complete characterization
...
1
2
3
4
5
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