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 Electronic Communications in Probability > Vol. 13 (2008) > Paper 19 open journal systems 


Symmetrization of Bernoulli

Soumik Pal, Cornell University


Abstract
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.


Full text: PDF

Pages: 194-197

Published on: April 9, 2008
Bibliography
  1. Kagan, Abram; Mallows, Colin L.; Shepp, Larry A.; Vanderbei, Robert J.; Vardi, Yehuda. Symmetrization of binary random variables. Bernoulli 5 (1999), no. 6, 1013--1020. MR1735782 (2001c:60020)
  2. Karatzas, Ioannis; Shreve, Steven E. Brownian motion and stochastic calculus.Second edition.Graduate Texts in Mathematics, 113. Springer-Verlag, New York, 1991. xxiv+470 pp. ISBN: 0-387-97655-8 MR1121940 (92h:60127)













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Electronic Communications in Probability. ISSN: 1083-589X