Parametric Estimation of Stochastic Differential Equations under Indirect Observability

间接可观性下随机微分方程的参数估计

• 批准号: 1109582
• 负责人: Ilya Timofeyev
• 金额: $ 19万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-01 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1109582&HistoricalAwards=false
• 关键词: Parametric; Estimation; Stochastic; Differential; Equations; Parametric; Estimation; Stochastic; Differential; Equations

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.

我们将开发数学形式主义，以估计由于大规模强迫的变化（应用于大规模结构），因此随机参数的参数波动。将选择强迫来模仿全球变暖的情况。因此，拟议的研究将阐明根据当今气候对其他气候条件估计的随机参数的有效性。我们提出了一种新型技术，用于从单独的（已解决）尺度的数据中估算小规模过程的随机参数化参数。在拟议的研究过程中，我们将为从大规模的时间序列的准确估算参数的准确估算而建立严格的数学基础。构图（也称为随机参数化）在大气和海洋的全球循环模型中起着重要作用。特别是，随机模型代表了小规模的物理过程，这些过程无法通过现代数值方法充分准确地解决。通常，这些随机模型中的参数是根据当今气候估算的。关键问题是随机参数将如何响应全球气候变化而变化。 特别是，如果观察的时间阶段太小，对大规模结构时间序列的随机模型的估计可能会失败。这是由于随机模型的轨迹和观察到的数据之间的基本差异。我们将开发数学技术来克服这个问题。