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Statistics for SPDEs

Markus Reiß (Mathematical Statistics, Humboldt-Universität zu Berlin)
Thursday 2 March 2023 11:15–12:00 Aud. G2 (1532-122)
Stochastics Seminar

Stochastic partial differential equations (SPDEs) are used more and more often to model real-world phenomena. Currently, statistical methodology for these equations driven by space-time white noise is developing rapidly. Based on the classical spectral method for parametric drift estimation, we shall exhibit fundamental differences with the case of stochastic ordinary differential equations. This method, however, is restricted to simple parametric situations and we discuss the local estimation method in detail, which allows to estimate varying coefficients in the differential operator of a parabolic SPDE nonparametrically with optimal rates. Extensions to deal with additional measurement errors and to estimate change points in the diffusivity are presented. As an application we consider cell motility experiments with repolarisation described by a stochastic Meinhardt model.

Organised by: Stochastics Group
Contact: Andreas Basse-O'Connor Revised: 25.05.2023