Studies in nonlinear stochastic processes. III. Approximate solutions of nonlinear stochastic differential equations excited by Gaussian noise and harmonic disturbances |
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Authors: | Aaron B Budgor |
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Institution: | (1) Department of Chemistry, University of California, San Diego La Jolla, California;(2) Present address: Lawrence Livermore Laboratory, University of California, Livermore, California |
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Abstract: | A fusion of the highly successful methods of harmonic and statistical linearization is used as a first approximation in determining, either iteratively or via a nonlinear integral equation, the effects of higher harmonics and non-Gaussian distortion terms on the second-order statistics of a wide variety of nonlinear stochastic differential equations perturbed by some linear combination of Gaussian noise and a periodic deterministic/stochastic excitation. Physical a posteriori applicability criteria are presented which justify when these higher order effects may be neglected. A simple modification of this statistical-harmonic linearization procedure based upon the Fokker-Planck variance is proposed.This work was supported in part by the National Science Foundation under grant CHE75-20624. |
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Keywords: | Nonlinear stochastic differential equation random noise harmonic excitation |
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