2021/01/30 by Mamikon S. Ginovyan, Ginovyan, Mamikon S., Murad S. Taqqu +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #60G10 #60G15 #62G05 #Bayesian Methods and Mixture Models #FOS: Mathematics #Financial Risk and Volatility Modeling #Functional Equations Stability Results #Mathematical Inequalities and Applications #Point processes and geometric inequalities #Primary: 60F05 #Probability (math.PR) #Stochastic processes and financial applications #secondary: 62F12
paper · pdf · doi:10.48550/arxiv.2102.00343
openalex publication_date 2021/01/30 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
This is a survey of recent results on central and non-central limit theorems\nfor quadratic functionals of stationary processes. The underlying processes are\nGaussian, linear or L 'evy-driven linear processes with memory, and are defined\neither in discrete or continuous time. We focus on limit theorems for Toeplitz\nand tapered Toeplitz type quadratic functionals of stationary processes with\napplications in parametric and nonparametric statistical estimation theory. We\ndiscuss questions concerning Toeplitz matrices and operators, Fej 'er-type\nsingular integrals, and L 'evy-It o-type and Stratonovich-type multiple\nstochastic integrals. These are the main tools for obtaining limit theorems.\n