Approximate controllability of a stochastic wave equation (Q1879300)

The equation is of the form \[ \varphi_{tt} = \Delta \varphi + \kappa(\varphi, \varphi_t, \nabla \varphi) + \psi + \sum_{j=1}^N (f_j + g_j \varphi) {dB_j \over dt} \] with Dirichlet boundary conditions, where \(\{B_j(t)\}\) is a set of Brownian motions which are mutually independent in a suitable sense. The author shows approximate controllability of the system, that is, existence of a control \(\psi\) that drives the system from an initial condition to a prescribed neighborhood of a target point. Among the tools used are the Hilbert uniqueness method and the martingale representation theorem.