In the previous chapters we saw that stochastic processes can be described using two equivalent approaches, one Lagrangian, leading to the Langevin equation, the other Eulerian, exemplified in the Fokker-Planck equation. Both descriptions allow to determine the stochastic properties of a system, provided that these properties are known at an earlier time. In addition, though, a third approach exists, where the evolution of a system in time is formulated by writing down the probability of observing a trajectory, or “path”, of its macroscopic variables. The first successful attempt to define path integration is due to Norbert Wiener, who in 1921 replaced the classical notion of a single, unique trajectory of a Brownian particle with a sum, or functional integral, over an infinity of possible trajectories, to compute the probability distribution describing the diffusion process (Wiener, Proc. Natl. Acad. Sci. USA 7:253, 294, 1921). In a second development, this concept was applied to quantum mechanics, first by Paul Dirac (Phys. Z. Sowjetunion 3, 1932) and then by Richard Feynman (Rev. Mod. Phys. 20:367, 1948), expressing the propagator of the Schrödinger equation in terms of a complex-valued path integral.