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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.

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rdf:type	topical concept yago:WikicatConceptsInPhysics yago:WikicatStochasticProcesses yago:Abstraction100002137 yago:Cognition100023271 yago:Concept105835747 yago:Content105809192 yago:Hypothesis105888929 yago:Idea105833840 yago:Model105890249 yago:PsychologicalFeature100023100 yago:StochasticProcess113561896
rdfs:label	System size expansion (en) 系统尺度展开 (zh)
rdfs:comment	系统尺度展开，又称van Kampen's展开或者Ω-展开，是由开创运用于随机过程分析的数学方法。它能够对一个具有非线性变化率系统的主方程的解进行估计。这种展开的第一个项被称为，此时系统主方程的解使用福克-普朗克方程（Fokker-Planck equation）进行估计，其线性估计系数由该系统的变化率和化学计量数决定。一般来讲，对于一个随机过程系统的数学描述是写下每个变量的微分方程，从而形成微分方程组（例如，在一个物理系统中，描述放射性分子随机衰变，或者在细胞环境中，描述基因的随机表达）。但是这样的微分方程组往往非常复杂，难以得到解析解，进而难以获得关于系统状态的统计量（例如，获取分子数目或者蛋白质数目的平均值或方差随时间变化的方程）。系统尺度展开可以运用统计的方法对这样的复杂的系统进行估计，从而得到该系统的近似解。 (zh) 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. (en)
dcterms:subject	Equations of physics Stoichiometry Applied mathematics Chemical kinetics Stochastic processes
Wikipage page ID	29803312 (xsd:integer)
Wikipage revision ID	1000484271 (xsd:integer)
Link from a Wikipage to another Wikipage	Probability distribution Protein-protein interaction Enzyme kinetics Allosteric regulation Ansatz Variance Covariance Operator (mathematics) Arithmetic mean Stochastic processes Stoichiometry Master equation Equations of physics Tuple Nico van Kampen Normal distribution Cellular compartment Cellular noise Fano factor Fokker–Planck equation Random variable Stoichiometry Intrinsic Noise Analyzer Applied mathematics Chemical kinetics Stochastic processes Index of dispersion Markov process Mean (statistics) Radioactive decay Nonlinear system Rate equation Protein-DNA interaction Taylor expansion
sameAs	System size expansion System size expansion System size expansion System size expansion System size expansion
dbp:wikiPageUsesTemplate	dbt:Reflist
has 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. (en) 系统尺度展开，又称van Kampen's展开或者Ω-展开，是由开创运用于随机过程分析的数学方法。它能够对一个具有非线性变化率系统的主方程的解进行估计。这种展开的第一个项被称为，此时系统主方程的解使用福克-普朗克方程（Fokker-Planck equation）进行估计，其线性估计系数由该系统的变化率和化学计量数决定。一般来讲，对于一个随机过程系统的数学描述是写下每个变量的微分方程，从而形成微分方程组（例如，在一个物理系统中，描述放射性分子随机衰变，或者在细胞环境中，描述基因的随机表达）。但是这样的微分方程组往往非常复杂，难以得到解析解，进而难以获得关于系统状态的统计量（例如，获取分子数目或者蛋白质数目的平均值或方差随时间变化的方程）。系统尺度展开可以运用统计的方法对这样的复杂的系统进行估计，从而得到该系统的近似解。 (zh)
gold:hypernym	Technique
prov:wasDerivedFrom	wikipedia-en:System_size_expansion?oldid=1000484271&ns=0
page length (characters) of wiki page	14618 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:System_size_expansion
is Link from a Wikipage to another Wikipage of	System Size Expansion Master equation Nico van Kampen Cellular noise Intrinsic Noise Analyzer Van Kampen's expansion Van Kampen's Omega-expansion Van Kampen's Omega expansion Omega-expansion Omega expansion
is Wikipage redirect of	System Size Expansion Van Kampen's expansion Van Kampen's Omega-expansion Van Kampen's Omega expansion Omega-expansion Omega expansion
is known for of	Nico van Kampen
is known for of	Nico van Kampen
is foaf:primaryTopic of	wikipedia-en:System_size_expansion

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