A central limit theorem for strictly stationary sequences in terms of slow variation in the limit

• Autorzy: Szewczak Z. S.
• Języki publikacji: EN

Abstrakty

EN

For strictly stationary random sequences satisfying the “minimal” dependence condition, necessary and sufficient conditions for the weak convergence to the normal law in terms of slow variation in the limit are found.

Słowa kluczowe

EN

stationary random sequences; limit theorem

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 1998
• Tom: Vol. 18, Fasc. 2
• Strony: 359--368
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Szewczak Z. S.

• Nicholas Copernicus University, NTC, ul., Chopina 12/18, 87-100 Toruń, Poland

Bibliografia

• [1] S. N. Bernstein, Sur l’extension du théoreme limite du calcul des probabilités aux sommes de quantités dépendantes, Math. Ann. 97 (1926), pp. 1-59.
• [2] M. Denker and A. Jakubowski, Stable limit distributions for strongly mixing sequences, Statist. Probab. Lett. 8 (1989), pp. 477-483.
• [3] W. Feller, On regular variation and local limit theorems, in: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, J. Neyman (Ed.), Vol. II, Part I, Univ. Calif. Press, Berkeley 1967, pp. 373-388.
• [4] — An Introduction to Probability Theory and Its Applications, Vol. II, 2nd edition, Wiley, New York 1971.
• [5] A. Jakubowski, Minimal conditions in p-stable limit theorems, Stochastic Process. Appl. 44 (1993), pp. 291-327.
• [6] — Minimal conditions in p-stable limit theorems. II, preprint 93-032, Bielefeld 1993.
• [7] — and Z. S. Szewczak, A Normal Convergence Criterion for strongly mixing stationary sequences, in: Limit Theorems in Probability and Statistics, Pécs (1989), Colloq. Math. Soc. János Bolyai 57 (1990), pp. 281-292.
• [8] A. V. Nagaev, Limit theorems for large deviations when Cramér condition does not hold, Izv. Akad. Nauk Uzbek. SSR 6 (1969), pp. 17-22.
• [9] W. M. Zolotarev, A Modern Theory of Summation of Independent Random Variables (in Russian), Nauka, Moscow 1986.