A variational approach to stochastic nonlinear problems |
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| Authors: | R Phythian W D Curtis |
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| Institution: | (1) Department of Physics, University College of Swansea, Singleton Park, SA2 8PP Swansea, UK |
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| Abstract: | A variational principle is formulated which enables the mean value and higher moments of the solution of a stochastic nonlinear differential equation to be expressed as stationary values of certain quantities. Approximations are generated by using suitable trial functions in this variational principle and some of these are investigated numerically for the case of a Bernoulli oscillator driven by white noise. Comparison with exact data available for this system shows that the variational approach to such problems can be quite effective. |
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| Keywords: | Stochastic nonlinear equations moments variational principle trial functions reserved variables statistical linearization |
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