Stationary solutions of linear ODEs with a randomly perturbed system matrix and additive noise
The paper considers systems of linear first-order ODEs with a randomly perturbed system matrix and stationary additive noise. For the description of the long-term behavior of such systems it is necessary to study their stationary solutions. We deal with conditions for the existence of stationary sol...
| Main Authors: | , |
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| Other Authors: | |
| Format: | Others |
| Language: | English |
| Published: |
Universitätsbibliothek Chemnitz
2005
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| Subjects: | |
| Online Access: | http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501335 http://nbn-resolving.de/urn:nbn:de:swb:ch1-200501335 http://www.qucosa.de/fileadmin/data/qucosa/documents/5055/data/t_04_st_wu.pdf http://www.qucosa.de/fileadmin/data/qucosa/documents/5055/20050133.txt |
| Summary: | The paper considers systems of linear first-order ODEs with a randomly perturbed system matrix and stationary additive noise. For the description of the
long-term behavior of such systems it is necessary to study their stationary solutions. We deal with conditions for the existence of stationary solutions as well as
with their representations and the computation of their moment functions.
Assuming small perturbations of the system matrix we apply perturbation techniques to find series representations of the stationary solutions and give asymptotic
expansions for their first- and second-order moment functions. We illustrate the findings with a numerical example of a scalar ODE, for which the moment functions of
the stationary solution still can be computed explicitly. This allows the assessment
of the goodness of the approximations found from the derived asymptotic expansions. |
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