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math.PR2021
A Survey on Limit Theorems for Toeplitz Type Quadratic Functionals of Stationary Processes and Applications
Mamikon S. Ginovyan, Murad S. Taqqu
This is a survey of recent results on central and non-central limit theorems for quadratic functionals of stationary processes. The underlying processes are Gaussian, linear or Lév…
math.PR2020
Extensions of Rosenblatt's results on the asymptotic behavior of the prediction error for deterministic stationary sequences
Nikolay M. Babayan, Mamikon S. Ginovyan, Murad S. Taqqu
One of the main problem in prediction theory of discrete-time second-order stationary processes is to describe the asymptotic behavior of the best linear mean squared predic…
math.PR2013
The Trace Problem for Toeplitz Matrices and Operators and its Impact in Probability
Mamikon S. Ginovyan, Artur A. Sahakyan, Murad S. Taqqu
The trace approximation problem for Toeplitz matrices and its applications to stationary processes dates back to the classic book by Grenander and Szegö, "Toeplitz forms and their…