The Borell–Ehrhard game

A precise description of the convexity of Gaussian measures is provided by sharp Brunn–Minkowski type inequalities due to Ehrhard and Borell. We show that these are manifestations of a game-theoretic mechanism: a minimax variational principle for Brownian motion. As an application, we obtain a Gauss...

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Bibliographic Details
Published in:Probability theory and related fields 2018-04, Vol.170 (3-4), p.555-585
Main Author: van Handel, Ramon
Format: Article
Language:English
Subjects:
Brownian motion
Convexity
Economics
Finance
Game theory
Insurance
Management
Mathematical and Computational Biology
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Minimax technique
Operations Research/Decision Theory
Probability
Probability Theory and Stochastic Processes
Quantitative Finance
Statistics for Business
Theoretical
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Summary:A precise description of the convexity of Gaussian measures is provided by sharp Brunn–Minkowski type inequalities due to Ehrhard and Borell. We show that these are manifestations of a game-theoretic mechanism: a minimax variational principle for Brownian motion. As an application, we obtain a Gaussian improvement of Barthe’s reverse Brascamp–Lieb inequality.
ISSN:0178-8051
1432-2064
DOI:10.1007/s00440-017-0762-4