  Inspired by path-integral solutions to the quantum relaxation problem, we
develop a numerical method to solve classical stochastic differential equations
with multiplicative noise that avoids averaging over trajectories. To test the
method, we simulate the dynamics of a classical oscillator multiplicatively
coupled to non-Markovian noise. When accelerated using tensor factorization
techniques, it accurately estimates the transition into the bifurcation regime
of the oscillator and outperforms trajectory-averaging simulations with a
computational cost that is orders of magnitude lower.
