I will outline a general mathematical framework for trajectory stratification of stochastic processes based on the non-equilibrium umbrella sampling method. Trajectory stratification involves decomposing trajectories of the underlying process into fragments limited to restricted regions of state space (strata), computing averages over the distributions of the trajectory fragments within the strata with minimal communication between them, and combining those averages with appropriate weights to yield averages with respect to the original underlying process. The result is an efficient and robust scheme for very general rare event simulation problems. Our framework reveals the full generality and flexibility of trajectory stratification, and it illuminates a common mathematical structure shared with the highly successful, equilibrium umbrella sampling method for free energy calculations.
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