Mathematics – Statistics Theory
Scientific paper
2011-11-08
Mathematics
Statistics Theory
27 pages, 8 figures, submitted Multiscale Model. Simul
Scientific paper
Consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective equation describing the dynamics on the longer diffusive time scale (homogenization framework). We consider the case where both the drift and the diffusion coefficients in the effective dynamics are space-dependent and depend on multiple unknown parameters. It is known that classical estimators, such as Maximum Likelihood and Quadratic Variation of the Path Estimators, fail to obtain reasonable estimates for parameters in the effective dynamics when based on observations of the underlying multiscale diffusion. We propose a novel algorithm for estimating both the drift and diffusion coefficients in the effective dynamics based on a semi-parametric framework. We demonstrate by means of extensive numerical simulations of a number of selected examples that the algorithm performs well when applied to data from a multiscale diffusion. The examples also illustrate that the algorithm can be used effectively to obtain accurate and unbiased estimates.
Kalliadasis Serafim
Krumscheid Sebastian
Pavliotis Grigorios A.
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