Characterization of probability distributions by Poincaré-type inequalities
Annales de l'I.H.P. Probabilités et statistiques (1987)
- Volume: 23, Issue: 1, page 91-110
- ISSN: 0246-0203
Access Full Article
topHow to cite
topReferences
top- [1] A.A. Borovkov and S.A. Utev, On an inequality and a related characterization of the normal distribution, Theory Prob. Appl., t. 28, 1984, p. 219-228. Zbl0533.60024
- [2] L.H.Y. Chen, An inequality for the multivariate normal distribution, J. Multivariate Anal., t. 12, 1982, p. 306-315. Zbl0483.60011MR661566
- [3] L.H.Y. Chen, Poincaré-type inequalities via stochastic integrals, Z. Wahrscheinlichkeitstheorie verw. Gebiete, t. 69, 1985, p. 251-277. Zbl0549.60019MR779459
- [4] H. Chernoff, A note on an inequality involving the normal distribution, Ann. Probab., t. 9, 1981, p. 533-535. Zbl0457.60014MR614640
- [5] M. Kac, Can one hear the shape of a drum? Amer. Math. Monthly, t. 73, 1966, p. 1-23. Zbl0139.05603MR201237
- [6] C. Stein, A bound for the error in the normal approximation to the distribution of a sum of dependent random variables, Proc. Sixth Berkeley Sympos. Math. Statist. Probab., t. 2, 1972, p. 583-602. Zbl0278.60026MR402873
- [7] H. Urakawa, Reflection groups and the eigenvalue problems of vibrating membranes with mixed boundary conditions, Tôhoku Math. Journ., t. 36, 1984, p. 175-183. Zbl0552.35014MR742592
Citations in EuDML Documents
top- Erwan Hillion, Oliver Johnson, Yaming Yu, A natural derivative on [0, n] and a binomial Poincaré inequality
- Aldéric Joulin, Nicolas Privault, Functional inequalities for discrete gradients and application to the geometric distribution
- Aldéric Joulin, Nicolas Privault, Functional inequalities for discrete gradients and application to the geometric distribution
- Aldo Goia, Ernesto Salinelli, Optimal nonlinear transformations of random variables