Coarse-grained modeling of multiscale diffusions : the p-variation estimates
Papavasiliou, Anastasia (2010) Coarse-grained modeling of multiscale diffusions : the p-variation estimates. Working Paper. Coventry: University of Warwick. Centre for Research in Statistical Methodology. (Working papers).
WRAP_Papavasiliou_10-05w.pdf - Published Version - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Official URL: http://www2.warwick.ac.uk/fac/sci/statistics/crism...
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  and avoids the subsampling step. The method is applied to a multiscale OU process.
|Item Type:||Working or Discussion Paper (Working Paper)|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Statistics|
|Library of Congress Subject Headings (LCSH):||Parameter estimation, Multiscale modeling|
|Series Name:||Working papers|
|Publisher:||University of Warwick. Centre for Research in Statistical Methodology|
|Place of Publication:||Coventry|
|Number of Pages:||18|
|Status:||Not Peer Reviewed|
|Access rights to Published version:||Open Access|
|References:|| R. Azencott, A. Beri and I. Timofeyev. Adaptive subsampling for parametric estimation of Gaussian Diffusions. Preprint.  J.P.N. Bishwal. Parameter Estimation in Stochastic Differential Equations. Lecture Notes in Mathematics vol. 1923, Springer, Berlin, 2008.  X. Chen. Limit Theorems for Functionals of Ergodic Markov Chains with General State Space. Memoirs of the AMS, vol. 129, No. 664, 1999.  D. Florens-Zmirou. Statistics on crossings of discretized diffusions and local time. Stochastic Process. Appl. 39: pp. 139–151, 1991.  M.I. Freidlin, A.D. Wentzell. Random perturbations of dynamical systems. Springer, New York, 1998.  S.E. Graversen and G. Peskir. Maximal Inequalities for the Ornstein-Uhlenbeck Process. Proceedings of the A.M.S. 128(10): pp. 3035–3041, 2000.  M. Katsoulakis, A. Majda and A. Sopasakis. Multiscale couplings in prototype hybrid deterministic/stochastic systems: Part 1, deterministic closures. Comm. Math. Sci. 2, pp. 255-294, 2004  M. Katsoulakis, A. Majda and A. Sopasakis. Multiscale couplings in prototype hybrid deterministic/stochastic systems: Part 2, stochastic closures. Comm. Math. Sci. 3, pp. 453-478, 2005.  Y.A. Kutoyants. Statistical inference for ergodic diffusion processes. Springer- Verlag, London, 2004.  J. Li, P.G. Kevrekidis, C.W. Gear and I.G. Kevrekidis. Deciding the nature of the coarse equation through microscopic simulations: the baby-bathwater scheme. SIAM Review, 49(3): pp. 469–487, 2007.  T. Lyons and Z. Qian. System control and rough paths. Oxford University Press, Oxford, 2002.  A.J. Majda, I. Timofeyev and E. Vanden-Eijnden. A mathematics framework for stochastic climate models. Comm. Pure Appl. Math. 54, pp. 891-974, 2001.  A.J. Majda, I. Timofeyev and E. Vanden-Eijnden. Stochastic models for selected slow variables in large deterministic systems. Nonlinearity 19, pp. 769-794, 2006.  A. Papavasiliou, G.A. Pavliotis and A.M. Stuart. Maximum likelihood drift estimation for multiscale diffusions. Stochastic Process. Appl. 119, pp. 3173–3210, 2009.  G.A. Pavliotis and A.M. Stuart. Parameter estimation for multiscale diffusions. J. Stat. Phys. 127, pp. 741–781, 2007.  G.A. Pavliotis and A.M. Stuart. Multiscale Methods: Averaging and Homogenization. Texts in Applied Mathematics 53, Springer, New York, 2008.  L.M. Ricciardi and S. Sato. First-passage-time density and moments of the Ornstein-Uhlenbeck process. J. Appl. Prob. 25, pp. 43–57, 1988.|
Actions (login required)