Activated processes driven by rare fluctuations are discussed in this thesis. Understanding the dynamics of these activated processes is important for understanding chemical and biological reactions, drug design and many other important applications. First, theoretical tools including the Langevin equation, the Fokker-Planck equation and the path integral technique are reviewed. Based on these theories, simulation methods have been developed to sample the activated processes by a number of investigators. Several of the most important path sampling and path generating approaches are introduced. A combination of analytic and numerical techniques are applied to study the distribution of the durations of transition events over a barrier in a one-dimensional system undergoing over-damped Langevin dynamics. Then we employ the ``weighted ensemble' path sampling method to generate an unbiased ensemble of paths for a conformational transition in a 210-dimensional model of the protein calmodulin, and also find the reaction rate. The results show that the weighted ensemble approach is a remarkably straightforward and successful method. At last, systems with multiple channels are studied by the weighted ensemble approach and the more common transition path sampling approach. The weighted ensemble method is distinguished by its ability to perform complete path sampling for systems with multiplechannels at reasonable cost.
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