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2008 Symmetrization of Bernoulli
Soumik Pal
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Electron. Commun. Probab. 13: 194-197 (2008). DOI: 10.1214/ECP.v13-1364


We show that an asymmetric Bernoulli random variable is symmetry resistant in the sense that any independent random variable, which when added to it produces a symmetric sum, must have a variance at least as much as itself. The main instrument is to use Skorokhod embedding to transfer the discrete problem to the realm of stochastic calculus.


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Soumik Pal. "Symmetrization of Bernoulli." Electron. Commun. Probab. 13 194 - 197, 2008.


Accepted: 9 April 2008; Published: 2008
First available in Project Euclid: 6 June 2016

zbMATH: 1189.60039
MathSciNet: MR2399281
Digital Object Identifier: 10.1214/ECP.v13-1364

Primary: 60E10

Keywords: Skorokhod embedding , symmetrization , symmetry resistant

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