Rules of calculus in the path integral representation of white noise Langevin equations
TYPEStatistical & Bio Seminar
Speaker:Vivien Lecomte
Affiliation:Université Grenoble-Alpes
Organizer:Yariv Kafri
Time:14:30 - 15:30
Location:Lidow Nathan Rosen (300)
The definition and manipulation of Langevin equations with multiplicative white noise require special care (one has to specify the time discretisation and a stochastic chain rule has to be used to perform changes of variables). While discretisation-scheme transformations and non-linear changes of variable can be safely performed on the Langevin equation, these same transformations lead to inconsistencies in its path-integral representation. We identify their origin and we show how to extend the well-known Itō prescription (dB²=dt) in a way that defines a modified stochastic calculus to be used inside the path-integral representation of the process, in its Onsager-Machlup form.
Joint work with Leticia Cugliandolo [arXiv:1704.03501]