Comparison of tail probabilities of strictly semistable/stable random vectors and their symmetrized counterparts with application

• Autorzy: Rajput B. S. , Rama-Murthy K.
• Języki publikacji: EN

Abstrakty

EN

It is shown that the tail probabilities of a strictly (r, a)-semistable (0 < r < 1, 0 < α < 2, α ≠ 1) Banach space valued random vector X and its symmetrized counterpart are ”uniformly” comparable in the sense that the constants appearing in the inequalities depend only on r and α (and not on X or the Banach space). Using this and some other known facts, several corollaries related to the moment inequalities of the random vector X and its symmetrized counterpart are obtained. The corresponding results for strictly α-stable Banach space valued random vectors, α ≠ 1, are also derived and discussed.

Słowa kluczowe

EN

stable; semistable; inequality

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2004
• Tom: Vol. 24, Fasc. 2
• Strony: 367--379
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Rajput B. S.

• Department of Mathematics, University of Tennessee, Knoxville, TN 37996

autor

Rama-Murthy K.

• Indian Statistical Institute, Bangalore, India

Bibliografia

• [1] A. Araujo and E. Giné, The CLT for Real and Banach Valued Random Variables, Wiley, New York 1980.
• [2] D. M. Chung, B. S. Rajput and A. Tortrat, Semi-stable laws on topological vector spaces, Z. Wahrsch. Verw. Gebiete 60 (1982), pp. 209-218.
• [3] E. Giné, M. B. Marcus and J. Zinn, A version of Chevet's Theorem for stable processes, J. Funct. Anal. 63 (1985), pp. 47-73.
• [4] W. Krakowiak, Operator semistable probability measures on Banach spaces, Colloq. Math. 43 (1980), pp. 351-363.
• [5] M. Lewandowski, M. Ryzner and T. Zak, Stable measure of a small ball, Proc. Amer. Math. Soc. 2 (1992), pp. 489-494.
• [6] W. Linde, Probability in Banach Spaces, Wiley, New York 1986.
• [7] B. S. Rajput, An estimate of the semistable measure of small balls in Banach spaces, in: Stochastic Processes and Functional Analysis, J. Goldstein et al. (Eds.), Dekker, New York, NY, 1997, pp. 171-178.
• [8] B. S. Rajput and K. Rama-Murthy, Spectral representations of semi-stable processes, and semi-stable laws on Banach spaces, J. Multivariate Anal. 21 (1987), pp. 141-159.
• [9] B. S. Rajput, K. Rama-Murthy and X. R. Retnam, Moment comparison of multilinear forms in stable and semi-stable random variables with application to semi-stable multiple integrals, in: Stochastic Processes and Related Topics (In memory of Stamatis Cambanis), I. Karatzas, B. S. Rajput, and M. S. Taqqu (Eds.], Birkhäuser, Boston, MA, 1998, pp. 339-355.
• [10] B. S. Rajput and J. Rosiński, Spectral representations of infinitely divisible processes, Probab. Theory Related Fields 82 (1989), pp. 451-487.
• [11] J. Rosiński, On series representation of infinitely divisible random vectors, Ann. Probab. 18 (1990), pp. 405-430.
• [12] G. Samorodnitsky and M. Taqqu, Stable Nan-Gaussian Random Processes, Chapman and Hall, New York, NY, 1994.