Parametric Estimation of Stochastic Differential Equations under Indirect Observability

我们将发展数学形式来估计随机参数化中由于大尺度强迫(应用于大尺度结构的强迫)的变化而引起的参数波动。强迫将被选择来模拟全球变暖的情景。因此，这项拟议的研究将阐明根据当前气候估计的随机参数在其他气候条件下的有效性。我们提出了一种新的技术，用于估计小尺度过程的随机参数，仅从大尺度(可分辨的)数据。在研究过程中，我们将为从大规模时间序列中准确估计参数建立严格的数学基础。随机模型(也称为随机参数化)在全球大气和海洋环流模型中扮演着重要的角色。特别是，随机模型代表的是小规模的物理过程，现代数值方法不能足够准确地解决这些过程。通常，这些随机模型中的参数是根据当前气候进行估计的。关键问题是随机参数化将如何改变以应对全球气候变化。特别是，如果观测的时间步长太小，从大型结构的时间序列估计随机模型可能会失败。这是由于随机模型的轨迹和观测数据之间的根本差异。我们将开发数学技术来克服这个问题。

We will develop mathematical formalism for estimating fluctuations in parameters in stochastic parametrizations due to changes in the large-scale forcing (forcing applied to the large-scale structures). The forcing will be chosen to mimic the global warming scenario. Therefore, the proposed research will elucidate the validity of stochastic parametrizations estimated from the present-day climate for other climatological conditions. We propose a novel technique for estimating parameters in stochastic parametrizations of small-scale processes from the data of the large (resolved) scales alone. In the course of the proposed research we will develop rigorous mathematical foundation for accurate estimation of parameters from the time-series of large scale.Stochastic models (also known as stochastic parametrizations) play an important role in Global Circulation Models of the atmosphere and ocean. In particular, stochastic models represent small-scale physical processes which cannot be sufficiently accurately resolved by modern numerical methods. Typically, parameters in these stochastic models are estimated from the present-day climate. The key question is how stochastic parametrizations will change in response to global climate change. In particular, estimation of stochastic models from time-series of large-scale structures can fail if the time-step of observation is too small. This is due to the fundamental differences between the trajectories of stochastic models and observed data. We will develop mathematical techniques to overcome this problem.