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 Electronic Communications in Probability > Vol. 10 (2005) > Paper 2 open journal systems 


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.


Full text: PDF

Pages: 7-16

Published on: February 24, 2005
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Electronic Communications in Probability. ISSN: 1083-589X