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Title: Summing over trajectories of stochastic dynamics with multiplicative noise

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:
;  [1] ;  [2] ;  [3]
  1. Department of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240 (China)
  2. (China)
  3. School of Biomedical Engineering, Shanghai Jiao Tong University, Shanghai 200240 (China)
Publication Date:
OSTI Identifier:
22419927
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BROWNIAN MOVEMENT; FOKKER-PLANCK EQUATION; LANGEVIN EQUATION; PROBABILITY