Wilhelm Stannat: Filtering SPDEs with Spatio-Temporal Point Process Observations

Speaker
Wilhelm Stannat, Berlin Institute of Technology

Abstract
I will introduce a mathematical framework for filtering problems arising from biophysical applications, where data is collected from confocal laser scanning microscopy recordings of the space-time evolution of intracellular wave dynamics of biophysical quantities. In these applications, signals are described by stochastic partial differential equations (SPDEs) and observations can be modelled as functionals of marked point processes whose intensities depend on the underlying signal. I will present the filtering equations for the unnormalized and the normalized conditions distribution, demonstrate the asymptotic consistency and approximations of finite dimensional observation schemes respectively partial observations. The theoretical results are validated through extensive simulations using synthetic and real data. I will also report on ongoing work on the associated combined state parameter estimation problem. The talk is based on jont work with Jan Szalankiewicz (TU Berlin) and Christina Martinez-Torres (U Potsdam).