Stewart Ethier
Limit theorems for Parrondo's paradox
That one can combine two losing games to form a
winning game is known as Parrondo's paradox. We
establish a strong law of large numbers and a central limit
theorem for the Parrondo player's cumulative profit,
both in a one-parameter family of profit-dependent games and
in a two-parameter family of history-dependent games, with
the winning game being either a random mixture or a
nonrandom pattern of the two losing games. We give formulas
for the mean and variance parameters of the central limit
theorem in nearly all such scenarios; formulas for the mean
permit an analysis of when the Parrondo effect is present.
(Joint work with Jiyeon Lee of Yeungnam University, South
Korea.)
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On 05 Jan 2009, 18:10.