Ito-Wiener chaos expansion with exact residual and correlation, variance inequalities
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We give a formula of expanding the solution of a stochastic differential equation (abbreviated as SDE) into a finite Ito-Wiener chaos with explicit residual. And then we apply this formula to obtain several inequalities for diffusions such as FKG type inequality, variance inequality and a correlation inequality for Gaussian measure. A simple proof for Houdre-Kagan's variance inequality for Gaussian measure is also given.
Hu, YZ. Ito-Wiener chaos expansion with exact residual and correlation, variance inequalities. JOURNAL OF THEORETICAL PROBABILITY. OCT 1997. 10(4):835-848.