Summing over trajectories of stochastic dynamics with multiplicative noise

Ying Tang, Ruoshi Yuan, Ping Ao

Published 2014-01-28Version 1

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.