A central limit theorem for multivariate strongly mixing random fields

• Autorzy: Tonelli C.
• Języki publikacji: EN

Abstrakty

EN

In this paper we extend a theorem of Bradley under interlaced mixing and strong mixing conditions. More precisely, we study the asymptotic normality of the normalized partial sum of an α-mixing strictly stationary random field of random vectors, in the presence of another dependence assumption.

Słowa kluczowe

EN

central limit theorem; α-mixing; random field of random vectors

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2010
• Tom: Vol. 30, Fasc. 2
• Strony: 215--222
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Tonelli C.

• Department of Mathematics, University of Louisville, 328 Natural Sciences Building, Louisville, KY 40292

Bibliografia

• [1] P. Billingsley, Probability and Measure, 3rd edition, Wiley, New York 1995.
• [2] P. Billingsley, Convergence of Probability Measures, 2nd edition, Wiley, New York 1999.
• [3] R. C. Bradley, Introduction to Strong Mixing Conditions, Vol. 1, Kendrick Press, 2007.
• [4] R. C. Bradley, Introduction to Strong Mixing Conditions, Vol. 3, Kendrick Press, 2007.
• [5] A. Bulinski and N. Kryzhanovskaya, Convergence rate in CLT for vector-valued random fields with self-normalization, Probab. Math. Statist. 26 (2006), pp. 261-281.
• [6] M. Peligrad, On the asymptotic normality of sequences of weak dependent random variables, J. Theoret. Probab. 9 (1996), pp. 703-715.
• [7] S. Utev and M. Peligrad, Maximal inequalities and an invariance principle for a class of weakly dependent random variables, J. Theoret. Probab. 16 (2003), pp. 101-115.