Rules of calculus in the path integral representation of white noise Langevin equations 
TYPE  Statistical & Bio Seminar 
Speaker:  Vivien Lecomte 
Affiliation:  Université GrenobleAlpes 
Organizer:  Yariv Kafri 
Date:  21.01.2018 
Time:  14:30  15:30 
Location:  Lidow Nathan Rosen (300) 
Abstract:  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 discretisationscheme transformations and nonlinear changes of variable can be safely performed on the Langevin equation, these same transformations lead to inconsistencies in its pathintegral representation. We identify their origin and we show how to extend the wellknown Itō prescription (dB²=dt) in a way that defines a modified stochastic calculus to be used inside the pathintegral representation of the process, in its OnsagerMachlup form.
Joint work with Leticia Cugliandolo [arXiv:1704.03501]
