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 Type | Technical report |
| Authors | |
| Author | Roberts, A. J. |
| Institution of Origin | University of Southern Queensland |
| Number of Pages | 30 |
| Year | 2007 |
| Publisher | University of Southern Queensland |
| Place of Publication | Toowoomba, 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. |
| Keywords | computer algebra, normal forms, stochastic differential equations |
| ANZSRC Field of Research 2020 | 490409. Ordinary differential equations, difference equations and dynamical systems |
| 490510. Stochastic analysis and modelling | |
| Public Notes | File reproduced in accordance with the copyright policy of the publisher/author. |
| Byline Affiliations | Computational Engineering and Science Research Centre |
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