Statistical analysis of tempo-spatial stochastic integral processes

• Applicant: Professorin Dr. Claudia Klüppelberg
• Subject Area: Mathematics
• Term: from 2016 to 2021
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 322862354

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.

• DFG Programme: Research Grants
• International Connection: Switzerland
• Cooperation Partner: Professor Dr. Carsten Chong