Computer algebra derives normal forms of stochastic differential equations

Technical report


Roberts, A. J.. 2007. Computer algebra derives normal forms of stochastic differential equations . Toowoomba, Australia. University of Southern Queensland.
Title

Computer algebra derives normal forms of stochastic differential equations

Report TypeTechnical report
Authors
AuthorRoberts, A. J.
Institution of OriginUniversity of Southern Queensland
Number of Pages30
Year2007
PublisherUniversity of Southern Queensland
Place of PublicationToowoomba, Australia
Abstract

[Abstract]: Modelling stochastic systems has many important applications. Normal form coordinate transforms are a powerful way to untangle interesting long term dynamics from undesirably detailed microscale dynamics. I aim to explore normal forms of stochastic differential equations when the dynamics has both slow modes and quickly decaying modes. The thrust is to derive normal forms useful for macroscopic modelling of detailed microscopic systems. Thus we not only must reduce the dimensionality of the dynamics, but also endeavour to remove all fast time processes. Sri Namachchivaya, Leng and Lin (1990­1 emphasise the importance of quadratic stochastic effects 'in order to capture the stochastic contributions of the stable modes to the drift terms of the critical modes.' I derive such important quadratic effects using the normal form coordinate transform to separate slow and fast modes. The results will help us accurately model multiscale stochastic systems.

Keywordscomputer algebra, normal forms, stochastic differential equations
ANZSRC Field of Research 2020490409. Ordinary differential equations, difference equations and dynamical systems
490510. Stochastic analysis and modelling
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Byline AffiliationsComputational Engineering and Science Research Centre
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