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（施加于大尺度结构的强迫）的变化而引起的参数波动。将选择强迫来模拟全球变暖的情景。因此，提出的研究将阐明从当前气候估计的随机参数化对其他气候条件的有效性。我们提出了一种新的技术来估计参数的随机参数化的小尺度过程从数据的大（分辨）尺度。在本研究的过程中，我们将为从大尺度时间序列中精确估计参数建立严格的数学基础。随机模式（也称为随机参数化）在大气和海洋的全球环流模式中起着重要的作用。特别是，随机模型代表了现代数值方法不能充分精确地解决的小尺度物理过程。通常，这些随机模式中的参数是根据当前气候估计的。关键问题是随机参数化将如何随着全球气候变化而变化。特别是，如果观测的时间步长过小，从大尺度结构的时间序列中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。我们将发展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.