Abstract

Infinite-dimensional stochastic calculus is often used to formalize space-time phenomena via stochastic evolution equations in function spaces. Yet, applications to the analysis of real data are rare. In this talk, we discuss practically relevant applications of infinite-dimensional stochastic calculus to the analysis of functional data and in particular, the role of stochastic evolution equations as nonparametric scaling limits for spatio-temporal high-frequency data. This can be used for the estimation of infinite-dimensional volatility models and dynamically consistent dimension reduction. We demonstrate the applicability and relevance of such methods in the context of bond market data.

The Talk is based on the articles
[1] Schroers, D.: Robust Functional Data Analysis for Stochastic Evolution Equations in Infinite Dimensions, available on arxiv:2401.16286, 2024.
[2] Benth, F.E., Schroers, D. and Veraart, A.E. D.: A feasible central limit theorem for realised covariation of SPDEs in the context of functional data, Annals of Applied Probabiliy 34 (2) (2024) 2208-2242.
[3] Benth, F.E., Schroers, D. and Veraart, A.E. D.: A weak law of large numbers for realised covariation in a Hilbert space setting, Stochastic Processes and their Applications 145 (2022) 241-268