Stable measure of a small ball
HTML articles powered by AMS MathViewer
- by M. Lewandowski, M. Ryznar and T. Żak PDF
- Proc. Amer. Math. Soc. 115 (1992), 489-494 Request permission
Abstract:
Let $\mu$ be a symmetric $p$-stable measure on a Banach space ($(E,||||)$. We prove that $\mu \{ ||x|| < t\} \leq Kt$, where the constant $K$ is independent of all properties of $\mu$ except for the measure of the unit ball $\mu \{ ||x|| < 1\}$.References
- T. W. Anderson, The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities, Proc. Amer. Math. Soc. 6 (1955), 170–176. MR 69229, DOI 10.1090/S0002-9939-1955-0069229-1 S. A. Chobanian, V. I. Tarieladze, and N. N. Vakhania, Probability distributions on Banach spaces, Reidel, Dordrecht, 1987. C. D. Hardin, Jr., Skewed stable variables and processes, Technical Report 79, Center for Stochastic Proc., Univ. of North Carolina, Chapel Hill, 1984.
- Raoul LePage, Michael Woodroofe, and Joel Zinn, Convergence to a stable distribution via order statistics, Ann. Probab. 9 (1981), no. 4, 624–632. MR 624688
- Werner Linde, Probability in Banach spaces—stable and infinitely divisible distributions, 2nd ed., A Wiley-Interscience Publication, John Wiley & Sons, Ltd., Chichester, 1986. MR 874529 J. Sawa, private communication, 1990.
- Stanisław J. Szarek, Condition numbers of random matrices, J. Complexity 7 (1991), no. 2, 131–149. MR 1108773, DOI 10.1016/0885-064X(91)90002-F
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 115 (1992), 489-494
- MSC: Primary 60B11
- DOI: https://doi.org/10.1090/S0002-9939-1992-1089410-5
- MathSciNet review: 1089410