Carleman and Observability Estimates for Stochastic Wave Equations

Based on a fundamental identity for stochastic hyperbolic-like operators, we derive in this paper a global Carleman estimate (with singular weight function) for stochastic wave equations. This leads to an observability estimate for stochastic wave equations with non-smooth lower order terms. Moreover, the observability constant is estimated by an explicit function of the norm of the involved coefficients in the equation.