  The problem of calculating real-time correlation functions is formulated in
terms of an imaginary-time partial differential equation. The latter is solved
analytically for the perturbed harmonic oscillator and compared with the known
exact result. The first order approximation for the short-time propagator is
derived and used for numerical solution of the equation by a Monte Carlo
integration. In general, the method provides a reformulation of the dynamic
sign problem, and is applicable to any two-time correlation function including
single-particle, density-density, current-current, spin-spin, and others. The
prospects of extending the technique onto multi-dimensional problems are
discussed.
