On the concentration of measure phenomenon for stable and related random vectors

Annals of Probability

Volumn 32, Issue 2, 2004, Pages 1496-1508

  Houdré, Christian ^a,b   Marchal, Philippe ^c  

^a UNIVERSITÉ PARIS EST CRÉTEIL   (France)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^c ECOLE NORMALE SUPÉRIEURE   (France)

Author keywords

Concentration of measure phenomenon; Infinite divisibility; Stable random vectors

Indexed keywords

EID: 3042551486     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/009117904000000289     Document Type: Article

References (8)

1. ARAUJO, A. and GINÉ, E. (1979). On tails and domains of attraction of stable measures in Banach spaces. Trans. Amer. Math. Soc. 248 105-119.
2. BINGHAM, N. H., GOLDIE, C. M. and TEUGELS, J. L. (1987). Regular Variation. Cambridge Univ. Press.
3. BORELL, C. (1975). The Brunn-Minkowski inequality in Gauss space. Invent. Math. 30 207-216.
4. HOUDRÉ, C. (2002). Remarks on deviation inequalities for functions of infinitely divisible random vectors. Ann. Probab. 30 1223-1237.
5. SAMORODNITSKY, G. and TAQQU, M. (1994). Stable Non-Gaussian Random Processes. Stochastic Models with Infinite Variance. Stochastic Modeling. Chapman and Hall, New York.
6. SATO, K.-I. (1999). Lévy Processes and Infinitely Divisible Distributions. Cambridge Univ. Press.
7. SUDAKOV, V. N. and TSIREL'SON, B. S. (1974). Extremal properties of half-spaces for spherically invariant measures. Zap. Nauch. Sem. LOMI 41 14-24. [English translation J. Soviet Math. 9 (1978) 9-18.]
8. SUDAKOV, V. N. and TSIREL'SON, B. S. (1974). Extremal properties of half-spaces for spherically invariant measures. Zap. Nauch. Sem. LOMI 41 14-24. [English translation J. Soviet Math. 9 (1978) 9-18.]