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.

随机过程建模在物理、生物和金融等领域有着广泛的应用。基于现有数据的随机过程模型的校准是必要的，以便使理论模型可供实践者使用。与此同时，随机过程的统计提出了有趣且具有挑战性的数学问题。本研究的目的是将数理统计和概率论的现代领域联系起来，以获得扩散、随机偏微分方程和lsamvy过程的新的估计方法和结果。更具体地说，我们希望为扩散模型中的非参数波动率估计构建自适应置信带，并利用所获得的见解来分析随机偏微分方程的估计量。同时，我们想扩展统计学习理论的概念，用于随机过程的推断。

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