  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.

Statistical Mechanics