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Studies in nonlinear stochastic processes. III. Approximate solutions of nonlinear stochastic differential equations excited by Gaussian noise and harmonic disturbances

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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.

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Author notes

  1. Aaron B. Budgor

    Present address: Lawrence Livermore Laboratory, University of California, Livermore, California

Authors and Affiliations

  1. Department of Chemistry, University of California, San Diego La Jolla, California

    Aaron B. Budgor

Authors
  1. Aaron B. Budgor
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Additional information

This work was supported in part by the National Science Foundation under grant CHE75-20624.

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Budgor, A.B. Studies in nonlinear stochastic processes. III. Approximate solutions of nonlinear stochastic differential equations excited by Gaussian noise and harmonic disturbances. J Stat Phys 17, 21–44 (1977). https://doi.org/10.1007/BF01089375

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  • DOI: https://doi.org/10.1007/BF01089375

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