title: Path summation formulation of the master equation.
abstract: Markovian dynamics, modeled by the kinetic master equation, has wide ranging applications in chemistry, physics, and biology. We derive an exact expression for the probability of a Markovian path in discrete state space for an arbitrary number of states and path length. The total probability of paths repeatedly visiting a set of states can be explicitly summed. The transition probability between states can be expressed as a sum over all possible paths connecting the states. The derived path probabilities satisfy the fluctuation theorem. The paths can be the starting point for a path space Monte Carlo procedure which can serve as an alternative algorithm to analyze pathways in a complex reaction network.
authors.affiliation: Department of Mechanical Engineering, Johns Hopkins University, Baltimore, Maryland 21218, USA.
authors.forename: Sean X
authors.initials: SX
authors.lastname: Sun
mesh_terms: D003198:Computer Simulation; D007700:Kinetics; D008390:Markov Chains; D008954:Models, Biological; D008956:Models, Chemical; D015233:Models, Statistical; D013269:Stochastic Processes