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Coarse-grained modeling of multiscale diffusions : the p-variation estimates
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Papavasiliou, Anastasia (2010) Coarse-grained modeling of multiscale diffusions : the p-variation estimates. In: Crisan, Dan, (ed.) Stochastic Analysis 2010. Dordrecht ; London: Springer Verlag, pp. 169-190. ISBN 9783642153570
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Official URL: http://dx.doi.org/10.1007/978-3-642-15358-7_8
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.
Item Type: | Book Item | ||||
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Divisions: | Faculty of Science, Engineering and Medicine > Science > Statistics | ||||
Publisher: | Springer Verlag | ||||
Place of Publication: | Dordrecht ; London | ||||
ISBN: | 9783642153570 | ||||
Book Title: | Stochastic Analysis 2010 | ||||
Editor: | Crisan, Dan | ||||
Official Date: | 2010 | ||||
Dates: |
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Number of Pages: | 299 | ||||
Page Range: | pp. 169-190 | ||||
DOI: | 10.1007/978-3-642-15358-7_8 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Restricted or Subscription Access |
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