Andreas Petersson: Nonparametric estimation of noise covariance in parabolic SPDEs

Speaker
Andreas Petersson, Linnaeus University

Abstract
An asymptotic limit theory is developed to estimate the incremental covariance kernel for linear parabolic stochastic partial differential equations (SPDEs) with additive colored noise using space-time infill asymptotics. The method is nonparametric, requiring only mild regularity assumptions on the kernel to ensure consistent estimation and asymptotic normality of the estimator. As an application, asymptotic tests on the covariance are constructed. This is joint work with Dennis Schroers.