Soit {u(t,x)}t≥0,x∈Rd la solution d’une équation de chaleur stochastique non-linéaire d-dimensionnelle, perturbée par un bruit gaussien, blanc en temps et avec une covariance homogène espace donnée mesure Borel finie qui satisfait condition Dalang. Nous démontrons deux théorèmes limite centrale fonctionnels pour des champs d’occupation forme N−d∫Rdg(u(t,x))ψ(x/N)dx quand N→∞, où g est function ...

Stochastic partial differential equations (SPDE) are used for stochastic modelling, for instance, in the study of neuronal behaviour in neurophysiology and in building stochastic models for turbulence. Huebner, Khasminskii and Rozovskii (1993) started the investigation of the maximum likelihood estimation of the parameters involved in two types of SPDE’s and extended their results for a class o...

The long term aim is to use modern dynamical systems theory to derive discretisations of noisy, dissipative partial differential equations. As a first step we here consider a small domain and apply stochastic centre manifold techniques to derive a model. The approach automatically parametrises subgrid scale processes induced by spatially distributed stochastic noise. It is important to discreti...