solidot新版网站常见问题,请点击这里查看。
消息
本文已被查看205次
Gaussian approximations for transition paths in Brownian dynamics. (arXiv:1604.06594v2 [math.PR] UPDATED)
来源于:arXiv
This paper is concerned with transition paths within the framework of the
overdamped Langevin dynamics model of chemical reactions. We aim to give an
efficient description of typical transition paths in the small temperature
regime. We adopt a variational point of view and seek the best Gaussian
approximation, with respect to Kullback-Leibler divergence, of the non-Gaussian
distribution of the diffusion process. We interpret the mean of this Gaussian
approximation as the "most likely path" and the covariance operator as a means
to capture the typical fluctuations around this most likely path.
We give an explicit expression for the Kullback-Leibler divergence in terms
of the mean and the covariance operator for a natural class of Gaussian
approximations and show the existence of minimisers for the variational
problem. Then the low temperature limit is studied via $\Gamma$-convergence of
the associated variational problem. The limiting functional consists of two
parts: The first part onl 查看全文>>