FKG Inequality for Brownian Motion and Stochastic Differential Equations
David Barbato, Università di Pisa, Italy
Abstract
The purpose of this work is to study some possible application of
FKG inequality to the Brownian motion and to Stochastic
Differential Equations. We introduce a special ordering on the
Wiener space and prove the FKG inequality with respect to this
ordering. Then we apply this result on the solutions Xt of a
stochastic differential equation with a positive coefficient
$sigma$ , we prove that these solutions Xt are increasing with
respect to the ordering, and finally we deduce a correlation
inequality between the solution of different stochastic equations.
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