Ilya Timofeyev (Houston)

Abstract:

In most of the work on estimation of stochastic differential equations from observational and/or numerical data it is typically assumed that the data can be accurately approximated by a stochastic differential equation on any time-step. Necessity to sub-sample the data arises when this is not the case, e.g. when it is desirable to approximate statistical properties of a smooth trajectory by a stochastic differential equation. In this case parametric estimation of an SDE would yield incorrect results if the discrete data is too dense in time. Therefore, the dataset has to be sub-sampled (i.e. rarefied).

We present two simple examples which demonstrate the issue if sub-sampling. While the sub-sampling criteria can be rigorously established for the first example, we also demonstrate that our analysis can be potentially extended to other systems.