Characterization of probability distributions by Poincaré-type inequalities

Louis H. Y. Chen

Annales de l'I.H.P. Probabilités et statistiques (1987)

  • Volume: 23, Issue: 1, page 91-110
  • ISSN: 0246-0203

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Chen, Louis H. Y.. "Characterization of probability distributions by Poincaré-type inequalities." Annales de l'I.H.P. Probabilités et statistiques 23.1 (1987): 91-110. <http://eudml.org/doc/77293>.

@article{Chen1987,
author = {Chen, Louis H. Y.},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {characterization of the normal distribution; infinitely divisible distributions},
language = {eng},
number = {1},
pages = {91-110},
publisher = {Gauthier-Villars},
title = {Characterization of probability distributions by Poincaré-type inequalities},
url = {http://eudml.org/doc/77293},
volume = {23},
year = {1987},
}

TY - JOUR
AU - Chen, Louis H. Y.
TI - Characterization of probability distributions by Poincaré-type inequalities
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1987
PB - Gauthier-Villars
VL - 23
IS - 1
SP - 91
EP - 110
LA - eng
KW - characterization of the normal distribution; infinitely divisible distributions
UR - http://eudml.org/doc/77293
ER -

References

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  1. [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. [2] L.H.Y. Chen, An inequality for the multivariate normal distribution, J. Multivariate Anal., t. 12, 1982, p. 306-315. Zbl0483.60011MR661566
  3. [3] L.H.Y. Chen, Poincaré-type inequalities via stochastic integrals, Z. Wahrscheinlichkeitstheorie verw. Gebiete, t. 69, 1985, p. 251-277. Zbl0549.60019MR779459
  4. [4] H. Chernoff, A note on an inequality involving the normal distribution, Ann. Probab., t. 9, 1981, p. 533-535. Zbl0457.60014MR614640
  5. [5] M. Kac, Can one hear the shape of a drum? Amer. Math. Monthly, t. 73, 1966, p. 1-23. Zbl0139.05603MR201237
  6. [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. [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

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