Large Toeplitz operators and quadratic forms generated by a stationary Gaussian sequence

Autor:	Valentin Solev, Léo Gerville-Réache
Rok vydání:	2006
Předmět:	Statistics and Probability Sequence Applied Mathematics General Mathematics Gaussian Spectral density Function (mathematics) Stationary sequence Toeplitz matrix Combinatorics symbols.namesake Operator (computer programming) Quadratic form symbols Mathematics
Zdroj:	Journal of Mathematical Sciences. 139:6625-6630
ISSN:	1573-8795 1072-3374
DOI:	10.1007/s10958-006-0378-1
Popis:	Let \(\Gamma _n (f,g) = \sum\limits_{ - n \leqslant t, s \leqslant n} {g_{t - s} X_t X_s } \) be a Toeplitz quadratic form generated by a real-valued function \(g(u) = \sum\limits_{ - \infty }^\infty {g_k e^{iku} } \) and a stationary sequence Xn with spectral density f. Many sufficient conditions for the asymptotic normality of the normalized quadratic form Ψn(f, g) have been proposed since 1958. The simplest one was given by L. Giraitis and D. Surgailis in 1990. Using the operator approach, we suggest a new vision of the problem and propose a new efficient condition on the pair of functions (f, g). Bibliography: 9 titles.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::84d270e32565ccdd626e9aaa144fefe1 https://doi.org/10.1007/s10958-006-0378-1 Zobrazit plný text záznamu Plný text ve formátu PDF