Computer algebra derives normal forms of stochastic differential equations

Roberts, A. J. (2007) Computer algebra derives normal forms of stochastic differential equations. Technical Report. University of Southern Queensland, Faculty of Sciences, Department of Maths and Computing , Toowoomba, Australia. [Report]


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[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.

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Item Type: Report (Technical Report)
Item Status: Live Archive
Additional Information: USQ publication.
Faculty / Department / School: Historic - Faculty of Sciences - Department of Maths and Computing
Date Deposited: 11 Oct 2007 00:53
Last Modified: 02 Jul 2013 22:40
Uncontrolled Keywords: computer algebra, normal forms, stochastic differential equations
Fields of Research : 01 Mathematical Sciences > 0101 Pure Mathematics > 010109 Ordinary Differential Equations, Difference Equations and Dynamical Systems
01 Mathematical Sciences > 0104 Statistics > 010406 Stochastic Analysis and Modelling

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