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FKG Inequality for Brownian Motion and Stochastic Differential Equations

   
@article{ECP1127,
	author = {David Barbato},
	title = {FKG Inequality for Brownian Motion and Stochastic Differential Equations},
	journal = {Electron. Commun. Probab.},
	fjournal = {Electronic Communications in Probability},
	volume = {10},
	year = {2005},
	keywords = {},
	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 $X_t$ 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.},
	pages = {no. 2, 7-16},
	issn = {1083-589X},
	doi = {10.1214/ECP.v10-1127},    
        url = {http://ecp.ejpecp.org/article/view/1127}}