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References (18)
-
Decompositions of random variables and random vectors -
I. Sidorov, Mikhail Fedori︠u︡k, M. Shabunin (1985)
Lectures on the theory of functions of a complex variable -
S. Bobkov, G. Chistyakov, F. Götze (2013)
Stability Problems in Cramér-Type Characterization in case of I.I.D. SummandsTheory of Probability and Its Applications, 57
-
A. Dembo, T. Cover, Joy Thomas (1991)
Information theoretic inequalitiesIEEE Trans. Inf. Theory, 37
-
H. McKean (1966)
Speed of approach to equilibrium for Kac's caricature of a Maxwellian gasArchive for Rational Mechanics and Analysis, 21
-
S. Bobkov, G. Chistyakov, F. Gotze (2015)
Regularized distributions and entropic stability of Cramer’s characterization of the normal lawStochastic Processes and their Applications, 126
-
W. Zwet, S. Geer, M. Wegkamp (2012)
Selected works of Willem van Zwet -
(1972)
Decompositions of random variables and random vectors. (Russian) Izd -
E. Carlen (1991)
Superadditivity of Fisher's information and logarithmic Sobolev inequalitiesJournal of Functional Analysis, 101
-
S. Bobkov, M. Madiman (2011)
On the problem of reversibility of the entropy power inequalityArXiv, abs/1111.6807
-
O. Johnson (2004)
Information Theory And The Central Limit Theorem -
K. Ball, P. Nayar, T. Tkocz (2015)
A reverse entropy power inequality for log-concave random vectorsarXiv: Probability
-
S. Bobkov, N. Gozlan, C. Roberto, P. Samson (2014)
Bounds on the deficit in the logarithmic Sobolev inequalityarXiv: Probability
-
S. Bobkov, M. Madiman (2011)
Reverse Brunn–Minkowski and reverse entropy power inequalities for convex measuresJournal of Functional Analysis, 262
-
Сергей Бобков, S. Bobkov, Геннадий Чистяков, G. Chistyakov, Фридрих Гетце, F. Götze (2012)
Stability problems in Cramér-type characterization in case of i.i.d. summands@@@Stability problems in Cramér-type characterization in case of i.i.d. summands, 57
-
T. Cover, Zhen Zhang (1994)
On the maximum entropy of the sum of two dependent random variablesIEEE Trans. Inf. Theory, 40
-
A. Stam (1959)
Some Inequalities Satisfied by the Quantities of Information of Fisher and ShannonInf. Control., 2
-
S. Bobkov, G. Chistyakov, F. Götze (2012)
Chapter 15 Entropic instability of Cramer’s characterization of the normal law
- Publisher
- Springer International Publishing
- Copyright
- © Springer International Publishing Switzerland 2016
- ISBN
- 978-3-319-40517-9
- Pages
- 3 –35
- DOI
- 10.1007/978-3-319-40519-3_1
- Publisher site
- See Chapter on Publisher Site
Abstract
[Optimal stability estimates in the class of regularized distributions are derived for the characterization of normal laws in Cramer’s theorem with respect to relative entropy and Fisher information distance.]
Published: Sep 22, 2016
Keywords: Characterization of normal laws; Cramer’s theorem; Stability problems