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July 2003 On Poisson equation and diffusion approximation 2
È. Pardoux, A. Yu. Veretennikov
Ann. Probab. 31(3): 1166-1192 (July 2003). DOI: 10.1214/aop/1055425774


Three different results are established which turn out to be closely connected so that the first one implies the second one which in turn implies the third one. The first one states the smoothness of an invariant diffusion density with respect to a parameter. The second establishes a similar smoothness of the solution of the Poisson equation in $\mathbb{R}^d$. The third one states a diffusion approximation result, or in other words an averaging of singularly perturbed diffusion for "fully coupled SDE systems'' or "SDE systems with complete dependence.''


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È. Pardoux. A. Yu. Veretennikov. "On Poisson equation and diffusion approximation 2." Ann. Probab. 31 (3) 1166 - 1192, July 2003.


Published: July 2003
First available in Project Euclid: 12 June 2003

zbMATH: 1054.60064
MathSciNet: MR1988467
Digital Object Identifier: 10.1214/aop/1055425774

Primary: 35B30 , 35J15 , 60H10 , 60J17

Keywords: diffusion approximation , Green function with parameter. , invariant density with parameter , Poisson equation with parameter

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 3 • July 2003
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