The Markov property of many Stochastic processes means that one can naturally construct a Path integral description. This can be used to draw parallels between stochastic processes and quantum mechanics.

From Langevin equation to path integrals

We begin with the general Langevin equation with no inertial term, but a deterministic force. We also assume the noise term is Gaussian white nosie

Ito/Stratonovitch dilemma and Multiplicative noise

See also

State-dependent diffusion: Thermodynamic consistency and its path integral formulation