Document Type: Research Paper

Author

Department of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran

Abstract

It is known that a stochastic differential equation (SDE) induces two probabilistic objects, namely a difusion process and a stochastic flow. While the diffusion process is determined by the in nitesimal mean and variance given by the coefficients of the SDE, this is not the case for the stochastic flow induced by the SDE. In order to characterize the stochastic flow uniquely the in nitesimal covariance given by the coefficients of the SDE is needed in addition. The SDEs we consider here are obtained by a weak perturbation of a rigid rotation by random elds which are white in time. In order to obtain information about the stochastic flow induced by this kind of multiscale SDEs we use averaging for the in nitesimal covariance. The main result here is an explicit determination of the coefficients of the averaged SDE for the case that the diffusion coefficients of the initial SDE are polynomial. To do this we develop a complex version of Cholesky decomposition algorithm.

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Main Subjects

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