Decomposition of stationary $\alpha$-stable random fields
نویسندگان
چکیده
منابع مشابه
Stationary Symmetric Α - Stable Discrete Parameter Random Fields
We establish a connection between the structure of a stationary symmetric α-stable random field (0 < α < 2) and ergodic theory of non-singular group actions, elaborating on a previous work by Rosiński (2000). With the help of this connection, we study the extreme values of the field over increasing boxes. Depending on the ergodic theoretical and group theoretical structures of the underlying ac...
متن کاملSpectral decomposition of locally stationary random processes
The notion of a locally stationary process is introduced by Silverman in [ l j . This is a new kind of a random process generalizing the notion of a weakly station ary process. Let {x(t)}, teR1bsa random process, generally complex, with vanishing mean value and finite covariance function R(s, t) = E{x(s) x(r)} on Wj x Mu where x(t) is the complex conjugate to x(r). The author of [ l j says tha...
متن کاملErgodic Properties of Sum– and Max– Stable Stationary Random Fields via Null and Positive Group Actions
We establish characterization results for the ergodicity of symmetric α–stable (SαS) and α–Fréchet max–stable stationary random fields. We first show that the result of Samorodnitsky [35] remains valid in the multiparameter setting, i.e., a stationary SαS (0 < α < 2) random field is ergodic (or equivalently, weakly mixing) if and only if it is generated by a null group action. The similarity of...
متن کاملKernel density estimation for stationary random fields
HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau...
متن کاملStationary random fields with linear regressions ∗
We analyze and identify stationary fields with linear regressions and quadratic conditional variances. We give sufficient conditions to determine one dimensional distributions uniquely as normal, and as certain compactly-supported distributions. Our technique relies on orthogonal polynomials, which under our assumptions turn out to be a version of the so called continuous q-Hermite polynomials.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2000
ISSN: 0091-1798
DOI: 10.1214/aop/1019160508