We review Parisi and Wu's stochastic quantisation procedure and apply it to the non-linear sigma model as well as the Yang-Mills model. We then review a number of recent results on the resulting equations. In particular, this sheds some new light on an old controversy regarding the interpretation of path integrals.
For further information, see https://www.math.ucla.edu/dls
The recorded talk can be accessed here: https://www.math.ucla.edu/dls/martin-hairer