Symmetric path integrals for stochastic equations with multiplicative noise

@article{Arnold2000SymmetricPI,
  title={Symmetric path integrals for stochastic equations with multiplicative noise},
  author={Arnold},
  journal={Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics},
  year={2000},
  volume={61 6 Pt A},
  pages={
          6099-102
        }
}
  • Arnold
  • Published 1 December 1999
  • Mathematics, Medicine, Physics
  • Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
A Langevin equation with multiplicative noise is an equation schematically of the form dq/dt=-F(q)+e(q)xi, where e(q)xi is Gaussian white noise whose amplitude e(q) depends on q itself. I show how to convert such equations into path integrals. The definition of the path integral depends crucially on the convention used for discretizing time, and I specifically derive the correct path integral when the convention used is the natural, time-symmetric one whose time derivatives are (q(t)-q(t-Deltat… 

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