Nonparametric estimation for semilinear SPDEs, namely stochastic reaction–diffusion equations in one space dimension, is studied. We consider observations of the solution field on a discrete grid time and with infill asymptotics both coordinates. Firstly, we derive nonparametric estimator reaction function underlying equation. The estimate chosen from finite-dimensional based least squares crit...

The chemical master equation (CME) is the exact mathematical formulation of chemical reactions occurring in a dilute and well-mixed volume. The reaction-diffusion master equation (RDME) is a stochastic description of reaction-diffusion processes on a spatial lattice, assuming well-mixing only on the length scale of the lattice. It is clear that, for the sake of consistency, the solution of the ...