Efficient computation of the first passage time distribution of the generalized master equation by steady-state relaxation.
The generalized master equation or the equivalent continuous time random walk equations can be used to compute the macroscopic first passage time distribution (FPTD) of a complex stochastic system from short-term microscopic simulation data. The computation of the mean first passage time and additional low-order FPTD moments can be simplified by directly relating the FPTD moment generating function to the moments of the local FPTD matrix. This relationship can be physically interpreted in terms of steady-state relaxation, an extension of steady-state flow. Moreover, it is amenable to a statistical error analysis that can be used to significantly increase computational efficiency. The efficiency improvement can be extended to the FPTD itself by modelling it using a gamma distribution or rational function approximation to its Laplace transform.
Shalloway
David
D
Biophysics Program, Department of Molecular Biology and Genetics, Cornell University, Ithaca, New York 14853, USA. dis2@cornell.edu
Faradjian
Anton K
AK
D000465:Algorithms; D001499:Bayes Theorem; D002627:Chemistry, Physical / Q000379:methods*; D003198:Computer Simulation; D003201:Computers; D007700:Kinetics; D008390:Markov Chains; D015233:Models, Statistical; D011336:Probability; D017510:Protein Folding; D012984:Software; D013269:Stochastic Processes; D013997:Time Factors