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Paper No. 10-5

Download 10-05

A Papavasiliou

Coarse-grained modeling of multiscale diffusions: the p-variation estimates

Date: February 2010

Abstract: We study the problem of estimating parameters of the limiting equation of a multiscale diffusion in the case of averaging and homogenization, given data from the corresponding multiscale system. First, we review some recent results that make use of the maximum likelihood of the limiting equation. In particular, it has been shown that in the averaging case, the MLE will be asymptotically consistent in the limit while in the homogenization case, the MLE will be asymptotically consistent only if we subsample the data. Then, we focus on the problem of estimating the diffusion coefficient. We suggest a novel approach that makes use of the total p-variation, as defined in [11] and avoids the subsampling step. The method is applied to a multiscale OU process.

Keywords: parameter estimation, multiscale diffusions, p-variation, Ornstein-Uhlenbeck.