Variance of set-indexed sums of mixing random variables and weak convergence of set-indexed processes
From MaRDI portal
Publication:1083116
DOI10.1214/aop/1176992440zbMath0604.60032OpenAlexW2049207421MaRDI QIDQ1083116
Charles M. Goldie, Prescilla E. Greenwood
Publication date: 1986
Published in: The Annals of Probability (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1214/aop/1176992440
mixing ratetightness lemmauniform integrability conditionsweak-convergence of continuous-path processes
Inequalities; stochastic orderings (60E15) Convergence of probability measures (60B10) Functional limit theorems; invariance principles (60F17)
Related Items (17)
Central limit theorems for stochastic processes under random entropy conditions ⋮ Exponential inequalities and functional central limit theorems for random fields ⋮ Further study strong consistency of \(M\) estimator in linear model for \(\tilde \rho\)-mixing random samples ⋮ Laws of the iterated logarithm for partial sum processes indexed by functions ⋮ On a CLT for Gibbs fields and its functional version. ⋮ Some strong limit theorems for \(\tilde \rho\)-mixing sequences of random variables ⋮ ON FUNCTIONAL CENTRAL LIMIT THEOREMS FOR LINEAR RANDOM FIELDS WITH DEPENDENT INNOVATIONS ⋮ On the spectral density and asymptotic normality of weakly dependent random fields ⋮ Chover-type laws of the \(k\)-iterated logarithm for \(\tilde {\rho }\)-mixing sequences of random variables ⋮ Some strong limit theorems for weighted product sums of \(\widetilde{\rho}\)-mixing sequences of random variables ⋮ Asymptotics for linear random fields ⋮ A central limit theorem for nonuniform \(\varphi\)-mixing random fields with infinite variance ⋮ The robust focused information criterion for strong mixing stochastic processes with \(\mathscr{L}^2\)-differentiable parametric densities ⋮ FIXED-b ASYMPTOTICS FOR SPATIALLY DEPENDENT ROBUST NONPARAMETRIC COVARIANCE MATRIX ESTIMATORS ⋮ Parallel and bootstrapped stochastic approximation ⋮ Minimum volume sets and generalized quantile processes ⋮ Kahane-Khintchine inequalities and functional central limit theorem for stationary random fields.
This page was built for publication: Variance of set-indexed sums of mixing random variables and weak convergence of set-indexed processes