Stochastic Quantisation is a not so well-known method for defining quantum mechanics and quantum field theory. It provides an interesting connection between Euclidean quantum field theory quantum field theory, as it is described by the Feynman path integral, and statistical mechanic. It may allow one to resolve some subtle questions that sometimes occur in the definition of the summation of all paths in the Feynman path integral, for instance in those cases where selfadjointness must be enforced. Some aspects of Stochastic Quantisation have some ressemblance with some ideas of topological field theory, which are a new chapter of quantum field theory.
For these 4 lectures, I will discuss some properties of Stochastic Quantisation, by starting from its basic definition trough Langevin and/or Fokker Planck equations, and by showing some examples of interest, especially for Chern-Simons like theories. I will also discuss the link of Stochastic Quantisation with twisted supersymmetry, when one tries to unify the stochastic time and the Euclidean physical space time coordinates. I will also show some new perspectives and possible new results that are opened by the existence of this formulation of quantum field theories.

References
Parisi and Wu-Yong Shi, Sci. Sin. （1981） 484.
E. Gozzi, Phys. Rev. D28 （1983）, 1922; D30 （1984）, 1218.
Baulieu and Grossman, Phys. Lett. B 212, （1988） 35.
Baulieu, Phys. Lett. B 232, （1989） 479.
Baulieu and Zwanziger, Nucl. Phys. B183 （1981） 163.