For its Winter 2026 term, the STOCHASTICA SNIP seminar will be held online every two weeks starting on October 14.  Talks of 30-45 minutes will be followed by 15-30 minutes of open discussion. Initially, seminars will be focused on introducing new problems and applications, to stimulate further discussions and ideas within individual working groups.  

This seminar is given by Wilhelm Stannat, TU Berlin, and chaired by Sonja Cox (WG2 leader).

State-parameter estimation of partially observed S(P)DE

We present a mathematical framework for filtering and parameter estimation of partially observed stochastic (partial) differential equations (S(P)DE), where observations are modelled as functionals of marked point processes whose intensities depend on the underlying signal. We derive both the unnormalized and normalized filtering equations for these systems. We subsequently analyze maximum-likelihood estimation (MLE) of drift parameters in the underlying S(P)DE. Using an
innovations representation, we express the observed-data score and Fisher information as functionals of the filter and its parameter sensitivity, avoiding joint state–parameter augmentation. For finite-dimensional linear–Gaussian diffusions (including Ornstein–Uhlenbeck models), we establish large-time identifiability, consistency of the online MLE, and a self-normalized central limit theorem. The theoretical results are illustrated with simulations using synthetic and real data collected from confocal laser scanning microscopy recordings of the space-time evolution of intracellular wave dynamics of biophysical quantities.

References:

[1] J. Szalankiewicz, C. Martinez-Torres, and W. Stannat. ”Filtering SPDEs with Spatio-Temporal Point Process Observations”. In: Stochastics and Partial Differential Equations: Analysis and Computations (2026), pp. 1-40. doi:10.1007/s40072-026-00418-y.
[2] J. Szalankiewicz, Inference for Partially Observed Stochastic Processes Filtering SPDEs with Marked Point Process Observations and Likelihood Theory under Partial Observation, PhD-thesis, TU Berlin (2026)
[3] G. Pasemann, C. Beta, and W. Stannat. ”Stochastic Reaction-Diffusion Systems in Biophysics: Towards a Toolbox for Quantitative Model Evaluation”. In: Nonlinear Dynamics for Biological Systems. Vol. 40. SEMA SIMAI Springer Series. Springer Cham, 2025, pp. 107-131. doi:10.1007/978-3-031-99044-1.