Cubification of nonlinear stochastic differential equations and approximate moments calculation of the Langevin Equation
| العنوان: | Cubification of nonlinear stochastic differential equations and approximate moments calculation of the Langevin Equation |
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| المؤلفون: | Pasquale Palumbo, Francesco Carravetta, Alessandro Borri |
| المساهمون: | Borri, A, Carravetta, F, Palumbo, P |
| المصدر: | CDC 55th IEEE Conference on Decision and Control (CDC16), pp. 4540–4545, Las Vegas, Nevada, USA, 12-14/12/2016 info:cnr-pdr/source/autori:Borri A.; Carravetta F.; Palumbo P./congresso_nome:55th IEEE Conference on Decision and Control (CDC16)/congresso_luogo:Las Vegas, Nevada, USA/congresso_data:12-14%2F12%2F2016/anno:2016/pagina_da:4540/pagina_a:4545/intervallo_pagine:4540–4545 |
| بيانات النشر: | Institute of Electrical and Electronics Engineers Inc., 2016. |
| سنة النشر: | 2016 |
| مصطلحات موضوعية: | 0301 basic medicine, Polynomial, Nonlinear method, Stochastic process, Mathematical analysis, Chemical Master Equation, Delay differential equation, Stochastic partial differential equation, Moment (mathematics), Langevin equation, 03 medical and health sciences, Stochastic differential equation, Moments computation, 030104 developmental biology, Ordinary differential equation, Langevin Equation, ING-INF/04 - AUTOMATICA, Nonlinear Systems, Mathematics |
| الوصف: | For the class of Ito-type nonlinear Stochastic Differential Equations (SDE), where the drift and the diffusion are ??-functions (??-SDE), we prove that the (infinite) set of all moments of the solution satisfies a system of infinite ordinary differential equations (ODEs), which is always linear. The result is proven by showing first that a ??-SDE can be cubified, i.e. reduced to a system of SDE of larger (but still finite) dimension in general, where drifts and diffusions are at most third-degree polynomial functions. Our motivation for deriving a moment equation in closed form comes from systems biology, where second-order moments are exploited to quantify the stochastic variability around the steady-state average amount of the molecular players involved in a bio-chemical reaction framework. Indeed, the proposed methodology allows to write the moment equations in the presence of non-polynomial nonlinarities, when exploiting the Chemical Langevin Equations (which are SDE) as a model abstraction. An example is given, associated to a protein-gene production model, where non-polynomial nonlinearities are known to occur. |
| اللغة: | English |
| URL الوصول: | https://explore.openaire.eu/search/publication?articleId=doi_dedup___::64551935cd8875da8f59f5409a9601df http://hdl.handle.net/10281/246644 |
| حقوق: | OPEN |
| رقم الأكسشن: | edsair.doi.dedup.....64551935cd8875da8f59f5409a9601df |
| قاعدة البيانات: | OpenAIRE |
| الوصف غير متاح. |