New statistical methods for stochastic processes

随机过程的新统计方法

• 批准号: 268709653
• 负责人: Professor Dr. Mathias Trabs
• 金额: --
• 依托单位: Institut für Stochastik
• 依托单位国家: 德国
• 项目类别: Research Fellowships
• 财政年份: 2014
• 资助国家: 德国
• 起止时间: 2013-12-31 至 2015-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/268709653?language=en
• 关键词: New; statistical; methods; stochastic; processes

The modeling with stochastic processes has rich applications in physics, biology and finance. The calibration of such stochastic process models based on the available data is essential in order to make the theoretical models accessible for the practitioners. At the same time statistics for stochastic processes poses interesting and challenging mathematical problems. The aim of this research fellowship is to connect modern fields in mathematical statistics and probability theory to obtain new estimation methods and results for diffusions, stochastic partial differential equations and Lévy processes. More specifically, we want to construct adaptive confidence bands for nonparametric volatility estimation in diffusion models and make use of the gained insights to analyze estimators for stochastic partial differential equations. In parallel we want to extend concepts of the statistical learning theory for inference on stochastic processes.

随机过程的建模在物理，生物学和金融中具有丰富的应用。基于可用数据的这种随机过程模型的校准对于使从业者可以访问理论模型至关重要。同时，随机过程的统计数据提出了有趣的和挑战数学问题。这项研究奖学金的目的是将数学统计和概率理论中的现代领域连接起来，以获取扩散，随机部分微分方程和Lévy过程的新估计方法和结果。更具体地说，我们希望在差异模型中构建自适应置信带，以进行非参数波动率估计，并利用所获得的见解来分析随机偏微分方程的估计器。同时，我们希望扩展统计学习理论的概念，以推断随机过程。

项目成果

Adaptive confidence bands for Markov chains and diffusions: Estimating the invariant measure and the drift

马尔可夫链和扩散的自适应置信带：估计不变测度和漂移

• DOI: 10.1051/ps/2016017
• 发表时间: 2016
• 期刊: arXiv: Statistics Theory
• 作者: J. Söhl;M. Trabs
• 通讯作者: M. Trabs

Spectral estimation for diffusions with random sampling times

具有随机采样时间的扩散的谱估计

• DOI: 10.1016/j.spa.2016.03.009
• 发表时间: 2016
• 期刊: arXiv: Statistics Theory
• 作者: J. Chorowski;M. Trabs
• 通讯作者: M. Trabs