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A martingale bound for the entropy associated with a trimmed filtration on Rd
Volume 1, Issue 2 (2014), pp. 151–165
Alexei Kulik   Taras Tymoshkevych  

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https://doi.org/10.15559/15-VMSTA16
Pub. online: 2 February 2015      Type: Research Article      Open accessOpen Access

Received
22 December 2014
Revised
18 January 2015
Accepted
19 January 2015
Published
2 February 2015

Abstract

Using martingale methods, we provide bounds for the entropy of a probability measure on ${\mathbb{R}}^{d}$ with the right-hand side given in a certain integral form. As a corollary, in the one-dimensional case, we obtain a weighted log-Sobolev inequality.

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© 2014 The Author(s). Published by VTeX
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Open access article under the CC BY license.

Keywords
Martingale entropy log-Sobolev inequality trimmed regions trimmed filtration

MSC2010
39B62 47D07 60E15 60J60

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