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An Improved Reynolds Technique for Approximate Solution of Linear Stochastic Differential Equations

Published online by Cambridge University Press:  19 July 2016

J. Stahlberg
Affiliation:
Astrophysikalisches Institut Potsdam Rosa Luxemburg Str.17a, D-O-1590 Potsdam, Germany

Extract

Our starting point is a formal linear stochastic differential equation of first order (higher order equations can be transformed to systems of these) where I, a, W are stochastic functions with and analogously for a and W. I, a, and W are allowed to depend on the element ω of a set Ω in which a probability measure is defined in the usual way (see e.g. Doob, 1953; de Witt-Morette, 1981). To get a solution of eq.(1) for the mean intensity we treat the problem according the Reynolds averaging technique in the usual manner : The stochastic equation is changed into an infinte hierarchical system of equations for the correlations.

Type
6. General Aspects of Dynamo Theory
Copyright
Copyright © Kluwer 1993 

References

De Witt-Morette, C., Elworthy, K.D.: 1981, Stochastic Diffential Equations, Proceedings of the “5-Tage-Kurs”, Bielefeld, University,Google Scholar
Doob, J.L.: 1953, Stochastic Processes, Wiley, New York,Google ScholarPubMed
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