Summing over trajectories of stochastic dynamics with multiplicative noise
arXiv:1401.7682 · doi:10.1063/1.4890968
Abstract
We demonstrate that the conventional path integral formulations generate inconsistent results exemplified by the geometric Brownian motion under the general stochastic interpretation. We thus develop a novel path integral formulation for the overdamped Langevin equation with the multiplicative noise. The present path integral leads to the corresponding Fokker-Planck equation, and naturally gives a normalized transition probability consistently in examples for general stochastic interpretations. Our result can be applied to study the fluctuation theorems and numerical calculations based on the path integral framework.
7 pages, 1 figure
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