SEMIPARAMETRIC DRIFT AND DIFFUSION ESTIMATION FOR MULTISCALE DIFFUSIONS
SEMIPARAMETRIC DRIFT AND DIFFUSION ESTIMATION FOR MULTISCALE DIFFUSIONS
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DOI：
10.1137/110854485
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发表时间：
2013-01-01
影响因子：
1.6
通讯作者：
Kalliadasis, S.
中科院分区：
文献类型：
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作者：
Krumscheid, S.;Pavliotis, G. A.;Kalliadasis, S.
本文研究了具有（至少）两个分离特征时间尺度的多尺度扩散过程的有效动力学的统计推断问题。更准确地说，我们试图确定在较长的扩散时间尺度上描述动态的有效方程中的参数，即，在一个同质化的框架中。我们研究的情况下，漂移和扩散系数的有效动态空间依赖性和依赖于多个未知参数。人们知道，经典的估计，如最大似然和二次变异的路径估计，无法获得合理的估计参数的有效动态时，根据观测的基础上的多尺度扩散。我们提出了一种新的算法估计漂移和扩散系数的有效动力学的基础上的半参数框架。我们证明了广泛的数值模拟的一些选定的例子，该算法表现良好，当应用到数据从多尺度扩散。这些例子也说明了该算法可以有效地用于获得准确和无偏的估计。
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 algorithm performs well when applied to data from a multiscale diffusion. These examples also illustrate that the algorithm can be used effectively to obtain accurate and unbiased estimates.