  Global dynamics in nonlinear stochastic systems is often difficult to analyze
rigorously. Yet, many excellent numerical methods exist to approximate these
systems. In this work, we propose a method to bridge the gap between
computation and analysis by introducing rigorous validated computations for
stochastic systems. The first step is to use analytic methods to reduce the
stochastic problem to one solvable by a deterministic algorithm and to
numerically compute a solution. Then one uses fixed-point arguments, including
a combination of analytical and validated numerical estimates, to prove that
the computed solution has a true solution in a suitable neighbourhood. We
demonstrate our approach by computing minimum-energy transition paths via
invariant manifolds and heteroclinic connections. We illustrate our method in
the context of the classical M\"uller-Brown test potential.
