Path summation formulation of the master equation.

@article{Sun2006PathSF,
  title={Path summation formulation of the master equation.},
  author={Sean X. Sun},
  journal={Physical review letters},
  year={2006},
  volume={96 21},
  pages={
          210602
        }
}
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… CONTINUE READING
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