title: Multidimensional master equation and its Monte-Carlo simulation.
abstract: We derive an integral form of multidimensional master equation for a markovian process, in which the transition function is obtained in terms of a set of discrete Langevin equations. The solution of master equation, namely, the probability density function is calculated by using the Monte-Carlo composite sampling method. In comparison with the usual Langevin-trajectory simulation, the present approach decreases effectively coarse-grained error. We apply the master equation to investigate time-dependent barrier escape rate of a particle from a two-dimensional metastable potential and show the advantage of this approach in the calculations of quantities that depend on the probability density function.
authors: Department of Physics, Beijing Normal University, Beijing 100875, People's Republic of China.
authors: Juan
authors: J
authors: Pang
authors: Zhan-Wu
authors: ZW
authors: Bai
authors: Jing-Dong
authors: JD
authors: Bao
mesh_terms: D008390:Markov Chains; D009010:Monte Carlo Method; D013997:Time Factors