Spectral representations of sum- and max-stable processes (Q626303)

Spectral representations of symmetric \(\alpha\)-stable (S\(\alpha\)S) and max-stable stochastic processes are considered. An association between a max-stable and the corresponding S\(\alpha\)S process is established in terms of spectral measures of their finite-dimensional distributions. The author investigates connections of ergodic properties of associated processes; e.g., a stationary max-stable process is ergodic iff the associated S\(\alpha\)S process is ergodic. The developed theory is based on the Hopf decomposition of nonsingular flows on measurable spaces. Applications to the theory of Brown-Resnik processes are considered.