Article PDF
References
Brown, B.M.: Martingale central limit theorems. Ann. Math. Statistics, 42, 59–66 (1971)
Brown, B.M., Eagleson, G.K.: Martingale convergence to infinitely divisible laws with finite variances. Trans. Amer. Math. Soc. 162, 449–453 (1971)
Dvoretzky, A.: Asymptotic normality for sums of dependent random variables. Proc. Sixth Berkeley Sympos. Math. Statist, and Probab. Vol. II, 513–536. Univ. of California Press (1972)
Jakubowski, A.: On limit theorems for sums of dependent Hilbert space valued random variables. Lecture Notes in Statistics, Vol. 2, 178–187. Berlin-Heidelberg-New York: Springer (1980)
Jakubowski, A., Kłopotowski, A.: Quelques remarques sur les démonstrations des théorèmes limite pour des vecteurs d-dimensionels aleatoires non indépendants. Publ. Sem. Proba. Univ. de Rennes (1980)
Kłopotowski, A.: Limit theorems for sums of dependent random vectors in ℝd. Dissert. Math. CLI, 1–62, PWN. Warszawa (1977)
Author information
Authors and Affiliations
Additional information
We thank Jean Jacod for his many critical and helpful remarks during the preparation of this paper.
Rights and permissions
About this article
Cite this article
Beśka, M., Kłopotowski, A. & Słomiński, L. Limit theorems for random sums of dependent d-dimensional random vectors. Z. Wahrscheinlichkeitstheorie verw Gebiete 61, 43–57 (1982). https://doi.org/10.1007/BF00537224
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00537224