Semiparametric Drift and Diffusion Estimation for Multiscale Diffusions
TLDR
In this paper, the authors consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales, and propose a novel algorithm for estimating both the drift and the diffusion coefficients in the effective dynamic equation.Abstract:
We 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, i.e., in a homogenization framework. We examine 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 the diffusion coefficients in the effective dynamics based on a semiparametric framework. We demonstrate by means of extensive numerical simulations of a number of selected examples that the a...read more
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