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L1-SMOOTHING FOR THE ORNSTEIN–UHLENBECK SEMIGROUP

Part of:Distribution theory - ProbabilityMiscellaneous applications of functional analysis

Published online by Cambridge University Press:  02 August 2012

K. Ball,
F. Barthe,
W. Bednorz,
K. Oleszkiewicz and
P. Wolff
K. Ball
Affiliation:
Mathematics Institute, University of Warwick, Coventry, CV4 7AL, U.K. (email: kmb120205@googlemail.com)
F. Barthe
Affiliation:
Institut de Mathématiques de Toulouse (CNRS UMR 5219), Université Paul Sabatier, 31062 Toulouse cedex 09, France (email: barthe@math.univ-toulouse.fr)
W. Bednorz
Affiliation:
Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, Poland (email: W.Bednorz@mimuw.edu.pl)
K. Oleszkiewicz
Affiliation:
Institute of Mathematics, University of Warsaw, Banacha 2, 02-097 Warszawa, PolandInstitute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland (email: K.Oleszkiewicz@mimuw.edu.pl)
P. Wolff
Affiliation:
Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa, Poland (email: pwolff@mimuw.edu.pl)

Abstract

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Given a probability density, we estimate the rate of decay of the measure of the level sets of its evolutes by the Ornstein–Uhlenbeck semigroup. The rate is faster than what follows from the preservation of mass and Markov’s inequality.

MSC classification

Secondary:46N30: Applications in probability theory and statistics60E15: Inequalities; stochastic orderings

Information

Type
Research Article
Information
Mathematika , Volume 59 , Issue 1 , January 2013, pp. 160 - 168
Copyright
Copyright © University College London 2012

References

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