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Coarse-Grained Modeling of Multiscale Diffusions: The p-Variation Estimates

In: Stochastic Analysis 2010

Author

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  • Anastasia Papavasiliou

    (University of Warwick, Department of Statistics
    University of Crete, Department of Applied Mathematics)

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 (“Lyons and Qian, System control and rough paths, Oxford University Press, Oxford, 2002”) and avoids the subsampling step. The method is applied to a multiscale OU process.

Suggested Citation

  • Anastasia Papavasiliou, 2011. "Coarse-Grained Modeling of Multiscale Diffusions: The p-Variation Estimates," Springer Books, in: Dan Crisan (ed.), Stochastic Analysis 2010, pages 169-190, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-15358-7_8
    DOI: 10.1007/978-3-642-15358-7_8
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