Study of the path probability of a Brownian motion
  This work is a numerical experiment of stochastic motion of conservative Hamiltonian system or weakly damped Brownian particles. The objective is to prove the existence of path probability and to compute its values. By observing a large number of particles moving from one point to another under Gaussian noise and conservative forces, it is determined that the path probability decreases exponentially with action along the paths. 
Lin Tongling, Pujos Cyril, Ou Congjie, Bi Wenping, Calvayrac Florent   and Wang Qiuping A
cond-mat.stat-mech