Itô-Wiener Chaos Expansion with Exact Residual and Correlation, Variance Inequalities |
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| Authors: | Yaozhong Hu |
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| Institution: | (1) Department of Mathematics, University of Kansas, 405 Snow Hall, Lawrence, Kansas, 66045 |
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| 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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| Keywords: | Wiener process Gaussian measure |
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