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2005 FKG Inequality for Brownian Motion and Stochastic Differential Equations
David Barbato
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Electron. Commun. Probab. 10: 7-16 (2005). DOI: 10.1214/ECP.v10-1127


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 $X_t$ of a stochastic differential equation with a positive coefficient $\sigma$, we prove that these solutions $X_t$ 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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David Barbato. "FKG Inequality for Brownian Motion and Stochastic Differential Equations." Electron. Commun. Probab. 10 7 - 16, 2005.


Accepted: 24 February 2005; Published: 2005
First available in Project Euclid: 4 June 2016

zbMATH: 1060.60015
MathSciNet: MR2119149
Digital Object Identifier: 10.1214/ECP.v10-1127

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