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- System_size_expansion 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.".
- System_size_expansion wikiPageID "29803312".
- System_size_expansion wikiPageLength "14093".
- System_size_expansion wikiPageOutDegree "42".
- System_size_expansion wikiPageRevisionID "687124279".
- System_size_expansion wikiPageWikiLink Allosteric_regulation.
- System_size_expansion wikiPageWikiLink Ansatz.
- System_size_expansion wikiPageWikiLink Arithmetic_mean.
- System_size_expansion wikiPageWikiLink Category:Applied_mathematics.
- System_size_expansion wikiPageWikiLink Category:Articles_created_via_the_Article_Wizard.
- System_size_expansion wikiPageWikiLink Category:Chemical_kinetics.
- System_size_expansion wikiPageWikiLink Category:Concepts_in_physics.
- System_size_expansion wikiPageWikiLink Category:Stochastic_processes.
- System_size_expansion wikiPageWikiLink Category:Stoichiometry.
- System_size_expansion wikiPageWikiLink Cellular_compartment.
- System_size_expansion wikiPageWikiLink Cellular_noise.
- System_size_expansion wikiPageWikiLink Coefficient_of_variation.
- System_size_expansion wikiPageWikiLink Covariance.
- System_size_expansion wikiPageWikiLink Enzyme_kinetics.
- System_size_expansion wikiPageWikiLink Fano_factor.
- System_size_expansion wikiPageWikiLink Fokker–Planck_equation.
- System_size_expansion wikiPageWikiLink Intrinsic_Noise_Analyzer.
- System_size_expansion wikiPageWikiLink Markov_process.
- System_size_expansion wikiPageWikiLink Master_equation.
- System_size_expansion wikiPageWikiLink Mean.
- System_size_expansion wikiPageWikiLink Nico_van_Kampen.
- System_size_expansion wikiPageWikiLink Nonlinear_system.
- System_size_expansion wikiPageWikiLink Operator_(mathematics).
- System_size_expansion wikiPageWikiLink Probability_distribution.
- System_size_expansion wikiPageWikiLink Protein–DNA_interaction.
- System_size_expansion wikiPageWikiLink Protein–protein_interaction.
- System_size_expansion wikiPageWikiLink Radioactive_decay.
- System_size_expansion wikiPageWikiLink Random_variable.
- System_size_expansion wikiPageWikiLink Rate_equation.
- System_size_expansion wikiPageWikiLink Stochastic_process.
- System_size_expansion wikiPageWikiLink Stoichiometry.
- System_size_expansion wikiPageWikiLink Taylor_series.
- System_size_expansion wikiPageWikiLink Tuple.
- System_size_expansion wikiPageWikiLink Variance.
- System_size_expansion wikiPageWikiLinkText "System size expansion".
- System_size_expansion wikiPageWikiLinkText "Van Kampen's system size expansion".
- System_size_expansion wikiPageWikiLinkText "approximations".
- System_size_expansion wikiPageWikiLinkText "system size expansion".
- System_size_expansion wikiPageUsesTemplate Template:Reflist.
- System_size_expansion subject Category:Applied_mathematics.
- System_size_expansion subject Category:Articles_created_via_the_Article_Wizard.
- System_size_expansion subject Category:Chemical_kinetics.
- System_size_expansion subject Category:Concepts_in_physics.
- System_size_expansion subject Category:Stochastic_processes.
- System_size_expansion subject Category:Stoichiometry.
- System_size_expansion hypernym Technique.
- System_size_expansion type TopicalConcept.
- System_size_expansion type Type.
- System_size_expansion type Concept.
- System_size_expansion type Field.
- System_size_expansion type Physic.
- System_size_expansion type Process.
- System_size_expansion type Redirect.
- System_size_expansion type Science.
- System_size_expansion type Type.
- System_size_expansion 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.".
- System_size_expansion label "System size expansion".
- System_size_expansion sameAs Q7663749.
- System_size_expansion sameAs m.0g5qk8_.
- System_size_expansion sameAs Q7663749.
- System_size_expansion wasDerivedFrom System_size_expansion?oldid=687124279.
- System_size_expansion isPrimaryTopicOf System_size_expansion.