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Publisher DOI: 10.1016/j.piutam.2016.03.023
Title: Analytical and semi-analytical solutions of some fundamental nonlinear stochastic differential equations
Language: English
Authors: Dostal, Leo 
Kreuzer, Edwin 
Keywords: stochastic averaging;Gaussian mixture;Duffing oscillator;stochastic differential equations;Hamiltonian system
Issue Date: 2016
Publisher: Elsevier
Source: Procedia IUTAM (19): 178-186 (2016-01-01)
Journal or Series Name: Procedia IUTAM 
Abstract (english): We are interested in perturbed Hamiltonian systems in a plane, which are damped and excited by an absolutely regular non-white Gaussian process. We use two methods for the determination of analytical and semi-analytical solutions to such nonlinear stochastic differential equations (SDE). The first method is based on a limit theorem by Khashminskii, from which a class of methods was derived known as stochastic averaging. From the drift and diffusion of the resulting averaged process, probability density functions and mean exit times can be easily obtained. The second method enables the determination of a Gaussian mixture representation for probability density functions of SDE's. This method was proposed by Pradlwarter and is known as Local Statistical Linearization. The error evolution of such Gaussian mixture shows promising results for further research.
Conference: IUTAM Symposium Analytical Methods in Nonlinear Dynamics 
DOI: 10.15480/882.1880
ISSN: 2210-9838
Institute: Mechanik und Meerestechnik M-13 
Type: (wissenschaftlicher) Artikel
License: CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives) CC BY-NC-ND 4.0 (Attribution-NonCommercial-NoDerivatives)
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