Rademacher chaos: Tail estimates versus limit theorems

Arkiv for Matematik

Volumn 42, Issue 1, 2004, Pages 13-29

  Blei, Ron ^a   Janson, Svante ^b  

^a UNIVERSITY OF CONNECTICUT   (United States)

^b UPPSALA UNIVERSITY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 2542590151     PISSN: 00042080     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02432908     Document Type: Article

References (20)

1. BECKNER, W., Inequalities in Fourier analysis, Ann. of Math. 102 (1975), 159-182.
2. BLEI, R., Analysis in Integer and Fractional Dimensions, Cambridge Studies in Advanced Mathematics 71. Cambridge Univ. Press, Cambridge, UK, 2001.
3. BLEI, R. and JANSON, S., Rademacher chaos: tail estimates vs limit theorems, Preprint, Institut Mittag-Leffler, Djursholm, 2001/2002.
4. P(G), Ann. Inst. Fourier (Grenoble) 20 (1970), 335-402.
5. DAVIE, A. M., Quotient algebras of uniform algebras, J. London Math. Soc. 7 (1973), 31-40.
6. HANSON, D. L. and WRIGHT, F. T., A bound on tail probabilities for quadratic forms in independent random variables, Ann. Math. Statist. 42 (1971), 1079-1083.
7. HITCZENKO, P., Domination inequality for martingale transforms of a Rademacher sequence, Israel J. Math. 84 (1993), 161-178.
8. JANSON, S., A functional limit theorem for random graphs with applications to subgraph count statistics, Random Structures Algorithms 1 (1990), 15-37.
9. JANSON, S., Orthogonal Decompositions and Functional Limit Theorems for Random Graph Statistics, Memoirs Amer. Math. Soc. 534, Amer. Math. Soc., Providence, RI, 1994.
10. JANSON, S., Gaussian Hilbert Spaces, Cambridge Tracts in Mathematics 129, Cambridge Univ. Press, Cambridge, 1997.
11. JOHNSON, G. W. and WOODWARD, G. S., On p-Sidon sets, Indiana Univ. Math. J. 24 (1974/75), 161-167.
12. KWAPIEŃ, S. and WOYCZYŃSKI, W. A., Random Series and Stochastic Integrals: Single and Multiple, Birkhäuser, Boston, MA, 1992.
13. LATALA, R., Tail and moment estimates for some types of chaos, Studia Math. 135 (1999), 39-53.
14. LITTLEWOOD, J. E., On bounded bilinear forms in an infinite number of variables, Q. J. Math. 1 (1930), 164-174.
15. MCLEISH, D. L., Dependent central limit theorems and invariance principles, Ann. Probab. 2 (1974), 620-628.
16. MONTGOMERY-SMITH, S. J., The distribution of Rademacher sums, Proc. Amer. Math. Soc. 109 (1990), 517-522.
17. NELSON, E., The free Markoff field, J. Funct. Anal. 12 (1973), 211-227.
18. DE LA PEÑA, V. H. and GINÉ, E., Decoupling. From Dependence to Independence. Randomly Stopped Processes. U-statistics and Processes. Martingales and Beyond, Springer-Verlag, New York, 1999.
19. RADEMACHER, H., Einige Sätze über Reihen von allgemeinen Orthogonalfunktionen, Math. Ann. 87 (1922), 112-138.
20. RUBIN, H. and VITALE, R. A., Asymptotic distribution of symmetric statistics, Ann. Statist. 8 (1980), 165-170.