Abstract
We give a formula of expanding the solution of a stochastic differential equation (abbreviated as SDE) into a finite Itô-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 Houdré-Kagan's variance inequality for Gaussian measure is also given.
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Hu, Y. Itô-Wiener Chaos Expansion with Exact Residual and Correlation, Variance Inequalities. Journal of Theoretical Probability 10, 835–848 (1997). https://doi.org/10.1023/A:1022654314791
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DOI: https://doi.org/10.1023/A:1022654314791