Limit theorems for filtered long-range dependent random fields
نویسندگان
چکیده
منابع مشابه
Central Limit Theorems for Dependent Random Variables
1. Limiting distributions of sums of 'small' independent random variables have been extensively studied and there is a satisfactory general theory of the subject (see e.g. the monograph of B.V. Gnedenko and A.N. Kolmogorov [2]). These results are conveniently formulated for double arrays Xn k (k = 1, . . . , kn ; n = 1, 2, . . . ) of random variables where the Xn k (k = 1, . . . , kn), the rand...
متن کاملExponential inequalities and functional central limit theorems for random fields
We establish new exponential inequalities for partial sums of random fields. Next, using classical chaining arguments, we give sufficient conditions for partial sum processes indexed by large classes of sets to converge to a set-indexed Brownian motion. For stationary fields of bounded random variables, the condition is expressed in terms of a series of conditional expectations. For non-uniform...
متن کاملLimit theorems for excursion sets of stationary random fields
We give an overview of the recent asymptotic results on the geometry of excursion sets of stationary random fields. Namely, we cover a number of limit theorems of central type for the volume of excursions of stationary (quasi–, positively or negatively) associated random fields with stochastically continuous realizations for a fixed excursion level. This class includes in particular Gaussian, P...
متن کاملCentral limit theorems for the excursion sets volumes of weakly dependent random fields
The multivariate central limit theorems (CLT) for the volumes of excursion sets of stationary quasi–associated random fields on R are proved. Special attention is paid to Gaussian and shot noise fields. Formulae for the covariance matrix of the limiting distribution are provided. A statistical version of the CLT is considered as well. Some numerical results are also discussed. AMS 2000 subject ...
متن کاملOn Functional Central Limit Theorems for Linear Random Fields with Dependent Innovations
For a linear random field (linear p-parameter stochastic process) generated by a dependent random field with zero mean and finite qth moments (q > 2p), we give sufficient conditions that the linear random field converges weakly to a multiparameter standard Brownian motion if the corresponding dependent random field does so. 2000 Mathematics subject classification: 60F17, 60G15.
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: Stochastics
سال: 2019
ISSN: 1744-2508,1744-2516
DOI: 10.1080/17442508.2019.1691211