Some limit theorems for partial sums of quadratic forms in stationary Gaussian variables
From MaRDI portal
Publication:4169998
DOI10.1007/BF00534252zbMath0388.60048OpenAlexW2016871973MaRDI QIDQ4169998
Publication date: 1979
Published in: Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/bf00534252
Sums of independent random variables; random walks (60G50) Limit theorems in probability theory (60F99)
Related Items (25)
On nonparametric regression for bivariate circular long-memory time series ⋮ On the limit distribution of the correlogram of a stationary Gaussian process with weak decrease in correlation ⋮ Prediction of long memory processes on same-realisation ⋮ Limit theorems for filtered long-range dependent random fields ⋮ Asymptotic distributions of the sample mean, autocovariances, and autocorrelations of long-memory time series ⋮ Variance of partial sums of stationary sequences ⋮ ON ASYMPTOTICS OF FUNCTIONALS OF RANDOM FIELDS WITH LONG-RANGE DEPENDENCE ⋮ Estimating the Mean Direction of Strongly Dependent Circular Time Series ⋮ Rosenblatt distribution subordinated to Gaussian random fields with long-range dependence ⋮ Generalized Hermite processes, discrete chaos and limit theorems ⋮ The trace problem for Toeplitz matrices and operators and its impact in probability ⋮ Covariances Estimation for Long-Memory Processes ⋮ Weak convergence of functionals of stationary long memory processes to Rosenblatt-type distributions ⋮ Sojourns of vector Gaussian processes inside and outside spheres ⋮ Estimation of the covariance function of Gaussian isotropic random fields on spheres, related Rosenblatt-type distributions and the cosmic variance problem ⋮ Limit theorems for non-linear functionals of Gaussian sequences ⋮ Limit theorems for Fourier transforms of functionals of Gaussian sequences ⋮ Necessary conditions for nonlinear functionals of Gaussian processes to satisfy central limit theorems ⋮ Limit theorems for Toeplitz-type quadratic functionals of stationary processes and applications ⋮ Self-similar random fields ⋮ Local empirical spectral measure of multivariate processes with long range dependence. ⋮ The law of the iterated logarithm for self-similar processes represented by multiple Wiener integrals ⋮ On a class of self-similar processes ⋮ Remarks on limit theorems for nonlinear functionals of Gaussian sequences ⋮ CLT and other limit theorems for functionals of Gaussian processes
Cites Work
- A representation for self-similar processes
- Gaussian and their subordinates self-similar random generalized fields
- Weak convergence to fractional brownian motion and to the rosenblatt process
- Fractional integrals of stationary processes and the central limit theorem
- Law of the iterated logarithm for sums of non-linear functions of Gaussian variables that exhibit a long range dependence
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: Some limit theorems for partial sums of quadratic forms in stationary Gaussian variables
