Motivation, Aims and Examples

These lectures will concentrate on (nonlinear) stochastic partial differential equations (SPDEs) of evolutionary type. All kinds of dynamics with stochastic infuence in nature or man-made complex systems can be modelled by such equations. As we shall see from the examples, at the end of this section the state spaces of their solutions are necessarily infinite dimensional such as spaces of (generalized) functions. In these notes the state spaces, denoted by E, will be mostly separable Hilbert spaces, sometimes separable Banach spaces.