Parameter Estimation for Semilinear Stochastic Partial Differential Equations

A theory of parametric inference for semilinear stochastic partial differential equations is developed, with special emphasis put on diffusivity estimation and its robustness to model uncertainty. Different measurement schemes are considered (spectral, local and discrete in space). The general theory is applicable, for example, to stochastic reaction-diffusion equations. Furthermore, stochastic activator-inhibitor systems, capable of generating traveling waves, are studied by means of simulated and experimental data from D. discoideum giant cells.

(based on joint work with S. Alonso, R. Altmeyer, C. Beta, I. Cialenco, S. Flemming, W. Stannat)