M ay 2 00 4 Integral representations of periodic and cyclic fractional stable motions ∗ † ‡
نویسنده
چکیده
Stable non-Gaussian self-similar mixed moving averages can be decomposed into several components. Two of these are the periodic and cyclic fractional stable motions which are the subject of this study. We focus on the structure of their integral representations and show that the periodic fractional stable motions have, in fact, a canonical representation. We study several examples and discuss questions of uniqueness, namely how to determine whether two given integral representations of periodic or cyclic fractional stable motions give rise to the same process.
منابع مشابه
Integral representations of periodic and cyclic fractional stable motions
Stable non-Gaussian self-similar mixed moving averages can be decomposed into several components. Two of these are the periodic and cyclic fractional stable motions which are the subject of this study. We focus on the structure of their integral representations and show that the periodic fractional stable motions have, in fact, a canonical representation. We study several examples and discuss q...
متن کاملIdentification of periodic and cyclic fractional stable motions
Self-similar stable mixed moving average processes can be related to nonsingular flows through their minimal representations. Self-similar stable mixed moving averages related to dissipative flows have been studied, as well as processes associated with identity flows which are the simplest type of conservative flows. The focus here is on self-similar stable mixed moving averages related to peri...
متن کامل1 9 M ay 2 00 8 Integral representations for a generalized Hermite linear functional ⋆
In this paper we find new integral representations for the generalized Hermite linear functional in the real line and the complex plane. As application, new integral representations for the Euler Gamma function are given.
متن کامل. D S ] 2 5 M ay 1 99 8 Time - Periodic Quasigeostrophic Motion under Dissipation and Forcing ∗
The quasigeostrophic equation is a prototypical geophysical fluid model. In this paper, we consider time-periodic motions of this model under dissipation and time-dependent wind forcing. We show that when the wind forcing is time-periodic and the spatial square-integral of the wind forcing is bounded in time, the full nonlinear quasigeostrophic model has time-periodic motions, under some condit...
متن کاملPeriodically correlated and multivariate symmetric stable processes related to periodic and cyclic flows
In this work we introduce and study discrete time periodically correlated stable processes and multivariate stationary stable processes related to periodic and cyclic flows. Our study involves producing a spectral representation and a spectral identification for such processes. We show that the third component of a periodically correlated stable process has a component related to a...
متن کامل