Introduction to stochastic partial differential equations

Magazine article, 2008

We introduce the Hilbert space-valued Wiener process and the corresponding stochastic integral of It\^o type. This is then used together with semigroup theory to obtain existence and uniqueness of weak solutions of linear and semilinear stochastic evolution problems in Hilbert space. Finally, this abstract theory is applied to the linear heat and wave equations driven by additive noise.