On the structure and representations of max-stable processes
By Yizao Wang, Stilian A. Stoev. Advances in Applied Probability, 2009
69 citations recorded by the source corpus.
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 latter two decompositions arise from connections to nonsingular flows and are closely related to the classification of stationary sum-stable processes. The interplay between the introduced decompositions of max-stable processes is further explored. As an example, the Brown-Resnick stationary processes, driven by fractional Brownian motions, are shown to be dissipative.
Subfields: Economics and Econometrics, Finance
View Paper: https://www.semanticscholar.org/paper/6ebded5a4ffd96b7f7db4b7e8d60b2e29acf5620
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In Economics and Econometrics
- A. C. Davison
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- C. Steinkohl
- Richard A. Davis
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In Finance
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Citations in the corpus
- Generalized Pickands constants and stationary max-stable processes (2016, background): “1 in [32] then yields that S < ∞ almost surely.”
- Extremes on river networks (2015, methodology): “Examples include mixed moving maxima processes (Wang and Stoev, 2010), Schlather processes (Schlather, 2002) and Brown–Resnick processes (Brown and Resnick, 1977; Kabluchko et al.”
- Statistical inference for max‐stable processes in space and time (2012, background): “Ergodic properties of Brown–Resnick processes have been studied for the uniparameter case in Stoev and Taqqu (2005) and Wang and Stoev (2010). The Brown–Resnick process (2) has a stochastic representation {∫ e”
- Conditional sampling for spectrally discrete max-stable random fields (2010, unknown): “[1], [6], [7], [9], [10], [13], [15], [16], [21], [24], [26], and [28], among many others.”