Importance sampling of rare transition events in Markov processes

We present an importance sampling technique for enhancing the efficiency of sampling rare transition events in Markov processes. Our approach is based on the design of an importance function by which the absolute probability of sampling a successful transition event is significantly enhanced, while preserving the relative probabilities among different successful transition paths. The method features an iterative stochastic algorithm for determining the optimal importance function. Given that the probability of sampling a successful transition event is enhanced by a known amount, transition rates can be readily computed. The method is illustrated in one- and two-dimensional systems.