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.

在该项目的更新时间，我们希望获得新的非参数估计方法的抛物线SPDE与高斯驱动噪声表现出的空间协方差比Riesz内核在原来的项目中考虑的平滑。这是从金融数学的动机，其中一个是关注建模远期利率的期限结构动态与利率衍生证券定价的目标。实证结果表明，利率期限结构的波动在时间上是不规则的，而在时间上是平滑的。基于高频数据，我们要构建一致的和渐近正态的随机波动率（和空间噪声相关指数）的估计证明极限定理的归一化功率变化的随机热方程在这个新的设置。

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