Generalizations of the fourth moment theorem

• Autorzy: Naganuma Nobuaki

Identyfikatory

DOI

10.37190/0208-4147.00060

• Języki publikacji: EN

Abstrakty

EN

Azmoodeh et al. established a criterion regarding convergence of the second and other even moments of random variables in a Wiener chaos with fixed order guaranteeing the central convergence of the random variables. This was a major step in studies of the fourth moment theorem. In this paper, we provide further generalizations of the fourth moment theorem by building on their ideas. More precisely, further criteria implying central convergence are provided: (i) the convergence of the fourth and any other even moment, (ii) the convergence of the sixth and some other even moments.

Słowa kluczowe

EN

fourth moment theorem; Nualart–Peccati criterion; central convergence; Wiener chaos

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2022
• Tom: Vol. 42, Fasc. 2
• Strony: 177--194
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Naganuma Nobuaki

• Kumamoto University 2-39-1, Kurokami Chuo-ku, Kumamoto 860-8555, Japan

Bibliografia

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• [10] F. W. J. Olver, D. W. Lozier, R. F. Boisvert, and C. W. Clark (eds.), NIST Handbook of Mathematical Functions, U.S. Department of Commerce, National Institute of Standards and Technology, Washington, DC, and Cambridge Univ. Press, Cambridge, 2010.
• [11] G. Peccati and C. A. Tudor, Gaussian limits for vector-valued multiple stochastic integrals, in: Séminaire de Probabilités XXXVIII, Lecture Notes in Math. 1857, Springer, Berlin, 2005, 247-262