TY  - UNPB
CY  - Toowoomba, Australia
N1  - USQ publication.
ID  - usqep31873
UR  - http://eprints.usq.edu.au/1873/
A1  - Roberts, A. J.
Y1  - 2007/01/23/
N2  - [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.

PB  - Univeristy of Southern Queensland, Department of Maths and Computing
KW  - computer algebra
KW  -  normal forms
KW  -  stochastic differential equations 
M1  - technical_report
TI  - Computer algebra derives normal forms of stochastic differential equations

AV  - public
EP  - 30
ER  -