  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.
