Limiting behavior of weighted sums of heavy-tailed random vectors and applications

• Autorzy: Pingyan C. , Scheffler H.-P.
• Języki publikacji: EN

Abstrakty

EN

We present an integral test to determine the limiting behavior of weighted sums of i.i.d. R^d-valued random vectors belonging to the (generalized) domain of operator semistable attraction of some nonnormal law, and deduce a version of Chover’s law of the iterated logarithm for them. As applications, the corresponding limit results for some classical summability methods are also established.

Słowa kluczowe

EN

generalized domains of semistable attraction; operator semistable laws; laws of the iterated logarithm; integral test

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2004
• Tom: Vol. 24, Fasc. 2
• Strony: 281--295
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Pingyan C.

• Department of Mathematics, Jinan University, Guangzhou, 510630, P.R. China

autor

Scheffler H.-P.

• Department of Mathematics, University of Nevada, Reno, NV 89557

Bibliografia

• [1] P. Y. Chen, Limiting behavior of weighted sums with stable distributions, Statist. Probab. Lett. 60 (2002), pp. 367-375.
• [2] P. Y. Chen and Q. P. Chen, LIL for φ-mixing sequence of random variables (in Chinese), Acta Math. Sinica 46 (3) (2003), pp. 571-580.
• [3] P. Y. Chen and L. H. Huang, On the law of the iterated logarithm for geometric series of stable distribution (in Chinese), Acta Math. Sinica 43 (2000), pp. 1063-1070.
• [4] P. Y. Chen and X. D. Liu, Law of the iterated logarithm for the weighted partial sums (in Chinese), Acta Math. Sinica 46 (5) (2003), pp. 999-1006.
• [5] P. Y. Chen and H. P. Scheffler, Limiting behavior of weighted sums of heavy-tailed random vectors, Publ. Math. Debrecen (2004), to appear.
• [6] P. Y. Chen and J. H. Yu, On Chover's LIL for the weighted sums of stable random variables, Acta Math. Sci. 23B (1) (2003), pp. 74-82.
• [7] V. Chorny, Operator semistable distributions on Rd, Theory Probab. Appl. 57 (1986), pp. 703-705.
• [8] J. Chover, A law of the iterated logarithm for stable summands, Proc. Amer. Math. Soc. 17 (1966), pp. 441-443.
• [9] M Ledoux and M. Talagrand, Probability in Banach Spaces, Springer, Berlin 1991.
• [10] D. Li, M. B. Rao, T. F. Jiang and X. C. Wang, Complete convergence and almost sure convergence of weighted sums of random variables, J. Theoret. Probab. 8 (1995), pp. 49-76.
• [11] M. M. Meerschaert and H. P. Scheffler, Limit Distributions for Sums of Independent Random Vectors, Wiley, New York 2001.
• [12] V. V. Peterov, Sums of Independent Random Variables, Springer, New York 1975.
• [13] H. P. Scheffler, A law of the iterated logarithm for heavy-tailed random vectors, Probab. Theory Related Fields 116 (2000), pp. 257-271.
• [14] H. P. Scheffler, Multivariate R-0 varying measures, Part I: Uniform bounds, Proc. London Math. Soc. 81 (2000), pp. 231-256.
• [15] H. P. Scheffler, Norming operators for generalized domains of semistable attraction, Publ. Math. Debrecen 58 (2001), pp. 391-409.