Decomposability for stable processes
Yizao Wang, Stilian A. Stoev, Parthanil Roy
TL;DR
This paper characterizes the decomposability of symmetric alpha-stable processes, identifying all possible independent components and extending the theory to max-stable processes, thus advancing understanding of their structural properties.
Contribution
It provides a comprehensive characterization of independent SaS components and develops a parallel theory for max-stable processes, filling a gap in the structural analysis of these processes.
Findings
All possible independent SaS components are characterized.
A parallel theory for max-stable processes is developed.
Results enhance understanding of the structural decomposability of stable processes.
Abstract
We characterize all possible independent symmetric alpha-stable (SaS) components of an SaS process, 0<alpha<2. In particular, we focus on stationary SaS processes and their independent stationary SaS components. We also develop a parallel characterization theory for max-stable processes.
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Taxonomy
TopicsStochastic processes and statistical mechanics · Stochastic processes and financial applications · Probability and Risk Models