  Matsubara Green's functions for interacting bosons are expressed as classical
statistical averages corresponding to a linear imaginary-time stochastic
differential equation. This makes direct numerical simulations applicable to
the study of equilibrium quantum properties of bosons in the non-perturbative
regime. To verify our results we discuss an oscillator with quartic
anharmonicity as a prototype model for an interacting Bose gas. An analytic
expression for the characteristic function in a thermal state is derived and a
Higgs-type phase transition discussed, which occurs when the oscillator
frequency becomes negative.
