Statistics of trajectories in two-state master equations

Andrew D. Jackson, Simone Pigolotti
2009 Physical Review E  
We derive a simple expression for the probability of trajectories of a master equation. The expression is particularly useful when the number of states is small and permits the calculation of observables that can be defined as functionals of whole trajectories. We illustrate the method with a two-state master equation, for which we calculate the distribution of the time spent in one state and the distribution of the number of transitions, each in a given time interval. These two expressions are
more » ... obtained analytically in terms of modified Bessel functions.
doi:10.1103/physreve.79.021121 pmid:19391720 fatcat:4phz7xiohbcxnmbevrbzn5fhjy