title: Summing over trajectories of stochastic dynamics with multiplicative noise.
abstract: We demonstrate that previous path integral formulations for the general stochastic interpretation generate incomplete results exemplified by the geometric Brownian motion. We thus develop a novel path integral formulation for the overdamped Langevin equation with multiplicative noise. The present path integral leads to the corresponding Fokker-Planck equation, and naturally generates a normalized transition probability in examples. Our result solves the inconsistency of the previous path integral formulations for the general stochastic interpretation, and can have wide applications in chemical and physical stochastic processes.
authors.affiliation: Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Ying
authors.initials: Y
authors.lastname: Tang
authors.affiliation: School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Ruoshi
authors.initials: R
authors.lastname: Yuan
authors.affiliation: Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China.
authors.forename: Ping
authors.initials: P
authors.lastname: Ao
mesh_terms: D008962:Models, Theoretical; D009038:Motion; D013269:Stochastic Processes