Statistical analysis of tempo-spatial stochastic integral processes

时空随机积分过程的统计分析

• 批准号: 322862354
• 负责人: Professorin Dr. Claudia Klüppelberg
• 金额: --
• 依托单位: The Hong Kong University of Science and Technology (HKUST)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/322862354?language=en
• 关键词: Statistical; analysis; tempo; spatial; stochastic

In the renewal time of the project, we want to derive new nonparametric estimation methods for parabolic SPDEs with a Gaussian driving noise exhibiting a spatial covariance that is smoother than the Riesz kernels considered in the original project. This is motivated from financial mathematics, where one is concerned with modeling term structure dynamics of forward rates with the objective of pricing interest rate derivative securities. Empirical observations suggest that fluctuations of the term structure should be smooth in the time to maturity while irregular in time. Based on high-frequency data, we want to construct consistent and asymptotically normal estimators for stochastic volatility (and the spatial noise correlation index) by proving limit theorems for the normalized power variations of the stochastic heat equation in this new setting.

在项目的更新时间，我们想要得到抛物型SPDEs的新的非参数估计方法，其中高斯型驱动噪声表现出比原项目中考虑的Riesz核更平滑的空间协方差。这是由金融数学推动的，其中一个人关注的是对远期利率的期限结构动态进行建模，目标是为利率衍生品证券定价。经验观察表明，期限结构的波动在期限结构上应该是平稳的，但在时间上是不规则的。基于高频数据，我们想要通过证明在这种新的背景下随机热方程的归一化功率变化的极限定理来构造随机波动率(和空间噪声相关指数)的相容和渐近正态估计。

项目成果

Normal approximation of the solution to the stochastic heat equation with Lévy noise

带 Lévy 噪声的随机热方程解的正态逼近

• DOI: 10.1007/s40072-019-00148-4
• 发表时间: 2020
• 期刊: Stochastics and Partial Differential Equations: Analysis and Computations
• 作者: C. Chong;T. Delerue
• 通讯作者: T. Delerue

Volterra-type Ornstein–Uhlenbeck processes in space and time

空间和时间上的沃尔泰拉型奥恩斯坦乌伦贝克过程

• DOI: 10.1016/j.spa.2017.10.012
• 发表时间: 2018
• 期刊: Stochastic Processes and their Applications
• 影响因子: 1.4
• 作者: V.-S. Pham;C. Chong
• 通讯作者: C. Chong

Estimation of causal continuous‐time autoregressive moving average random fields

• DOI: 10.1111/sjos.12444
• 发表时间: 2020-01
• 期刊: Scandinavian Journal of Statistics
• 影响因子: 1
• 作者: C. Klüppelberg;V. Pham

High-frequency analysis of parabolic stochastic PDEs

• DOI: 10.1214/19-aos1841
• 发表时间: 2018-06
• 期刊: The Annals of Statistics
• 作者: Carsten Chong