Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 50, Issue 34, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8121/aa7dd6
Keywords
Langevin equation; Stochastic processes; path-integral formalism; Stochastic chain rule; Onsager-Machlup functional
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Funding
- ERC Starting Grant [680275 MALIG, ANR-15-CE40-0020-03]
- UGA IRS PHEMIN project
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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 Ito prescription (dB(2) = dt) in a way that defines a modified stochastic calculus to be used inside the pathintegral representation of the process, in its Onsager-Machlup form.
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