This work is concerned with the similarity between the two important reduction schemes: optimal prediction and stochastic averaging. To this end, we consider a randomly perturbed Hamiltonian system and derive a generalized Langevin equation from a Kolmogorov backward equation. We then show the similarity by adopting conditional expectation as our projection operator in the generalized Langevin equation. The characteristics of the conditional expectation play a central role in our study.
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.Copyright © 2007
by American Society of Mechanical Engineers
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