Short-time expansion of one-dimensional ...
Document type :
Compte-rendu et recension critique d'ouvrage
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Title :
Short-time expansion of one-dimensional Fokker-Planck equations with heterogeneous diffusion
Author(s) :
Dupont, Tom [Auteur]
Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 [IEMN]
Centrale Lille
Giordano, Stefano [Auteur]
Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN [AIMAN-FILMS - IEMN]
Cleri, Fabrizio [Auteur]
Physique - IEMN [PHYSIQUE - IEMN]
Blossey, Ralf [Auteur]
Unité de Glycobiologie Structurale et Fonctionnelle - UMR 8576 [UGSF]
Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 [IEMN]
Centrale Lille
Giordano, Stefano [Auteur]
![refId](/themes/Mirage2//images/idref.png)
Acoustique Impulsionnelle & Magnéto-Acoustique Non linéaire - Fluides, Interfaces Liquides & Micro-Systèmes - IEMN [AIMAN-FILMS - IEMN]
Cleri, Fabrizio [Auteur]
![refId](/themes/Mirage2//images/idref.png)
Physique - IEMN [PHYSIQUE - IEMN]
Blossey, Ralf [Auteur]
![refId](/themes/Mirage2//images/idref.png)
Unité de Glycobiologie Structurale et Fonctionnelle - UMR 8576 [UGSF]
Journal title :
Physical Review E : Statistical, Nonlinear, and Soft Matter Physics
Pages :
064106
Publisher :
American Physical Society
Publication date :
2024
ISSN :
1539-3755
HAL domain(s) :
Physique [physics]/Matière Condensée [cond-mat]/Mécanique statistique [cond-mat.stat-mech]
Physique [physics]/Physique [physics]/Biophysique [physics.bio-ph]
Physique [physics]/Physique [physics]/Biophysique [physics.bio-ph]
English abstract : [en]
We formulate a short-time expansion for one-dimensional Fokker-Planck equations with spatially dependent diffusion coefficients, derived from stochastic processes with Gaussian white noise, for general values of the ...
Show more >We formulate a short-time expansion for one-dimensional Fokker-Planck equations with spatially dependent diffusion coefficients, derived from stochastic processes with Gaussian white noise, for general values of the discretization parameter 0 ⩽ α ⩽ 1 of the stochastic integral. The kernel of the Fokker-Planck equation (the propagator) can be expressed as a product of a singular and a regular term. While the singular term can be given in closed form, the regular term can be computed from a Taylor expansion whose coefficients obey simple ordinary differential equations. We illustrate the application of our approach with examples taken from statistical physics and biophysics. Further, we show how our formalism allows to define a class of stochastic equations which can be treated exactly. The convergence of the expansion cannot be guaranteed independently from the discretization parameter α.Show less >
Show more >We formulate a short-time expansion for one-dimensional Fokker-Planck equations with spatially dependent diffusion coefficients, derived from stochastic processes with Gaussian white noise, for general values of the discretization parameter 0 ⩽ α ⩽ 1 of the stochastic integral. The kernel of the Fokker-Planck equation (the propagator) can be expressed as a product of a singular and a regular term. While the singular term can be given in closed form, the regular term can be computed from a Taylor expansion whose coefficients obey simple ordinary differential equations. We illustrate the application of our approach with examples taken from statistical physics and biophysics. Further, we show how our formalism allows to define a class of stochastic equations which can be treated exactly. The convergence of the expansion cannot be guaranteed independently from the discretization parameter α.Show less >
Language :
Anglais
Popular science :
Non
Source :
Submission date :
2024-06-18T03:46:33Z
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