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- Q7663749 subject Q6991034.
- Q7663749 subject Q7020694.
- Q7663749 subject Q7163675.
- Q7663749 subject Q7478371.
- Q7663749 subject Q8806217.
- Q7663749 subject Q8980764.
- Q7663749 abstract "The system size expansion, also known as van Kampen's expansion or the Ω-expansion, is a technique pioneered by Nico van Kampen used in the analysis of stochastic processes. Specifically, it allows one to find an approximation to the solution of a master equation with nonlinear transition rates. The leading order term of the expansion is given by the linear noise approximation, in which the master equation is approximated by a Fokker–Planck equation with linear coefficients determined by the transition rates and stoichiometry of the system.Less formally, it is normally straightforward to write down a mathematical description of a system where processes happen randomly (for example, radioactive atoms randomly decay in a physical system, or genes that are expressed stochastically in a cell). However, these mathematical descriptions are often too difficult to solve for the study of the systems statistics (for example, the mean and variance of the number of atoms or proteins as a function of time). The system size expansion allows one to obtain an approximate statistical description that can be solved much more easily than the master equation.".
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- Q7663749 wikiPageWikiLink Q6991034.
- Q7663749 wikiPageWikiLink Q7020694.
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- Q7663749 comment "The system size expansion, also known as van Kampen's expansion or the Ω-expansion, is a technique pioneered by Nico van Kampen used in the analysis of stochastic processes. Specifically, it allows one to find an approximation to the solution of a master equation with nonlinear transition rates.".
- Q7663749 label "System size expansion".