Diffusion Parameter Estimation for the Homogenized Equation
Theodoros Manikas, Anastasia Papavasiliou · Multiscale Modeling and Simulation · 2019
We construct a novel estimator for the diffusion coefficient of the limiting homogenized equation, when observing the slow dynamics of a multiscale model, in the case when the slow dynamics are of bounded variation. Previous research suggests subsampling the data on fixed intervals and computing the corresponding quadratic variation. However, to achieve optimality, this approach requires knowledge of the scale separation variable. Instead, we suggest computing the quadratic variation corresponding to the local extrema of the slow process. Our approach results in a natural subsampling and avoids the issue of choosing a subsampling rate. We prove that the estimator is asymptotically unbiased and we numerically demonstrate that its $L_2$-error is smaller than the one achieved by subsampling homogeneously.