# An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations

Yves Frederix; Giovanni Samaey; Dirk Roose

- Volume: 45, Issue: 3, page 541-561
- ISSN: 0764-583X

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topFrederix, Yves, Samaey, Giovanni, and Roose, Dirk. "An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 45.3 (2011): 541-561. <http://eudml.org/doc/273243>.

@article{Frederix2011,

abstract = {We consider multiscale systems for which only a fine-scale model describing the evolution of individuals (atoms, molecules, bacteria, agents) is given, while we are interested in the evolution of the population density on coarse space and time scales. Typically, this evolution is described by a coarse Fokker-Planck equation. In this paper, we consider a numerical procedure to compute the solution of this Fokker-Planck equation directly on the coarse level, based on the estimation of the unknown parameters (drift and diffusion) using only appropriately chosen realizations of the fine-scale, individual-based system. As these parameters might be space- and time-dependent, the estimation is performed in every spatial discretization point and at every time step. If the fine-scale model is stochastic, the estimation procedure introduces noise on the coarse level. We investigate stability conditions for this procedure in the presence of this noise and present an analysis of the propagation of the estimation error in the numerical solution of the coarse Fokker-Planck equation.},

author = {Frederix, Yves, Samaey, Giovanni, Roose, Dirk},

journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},

keywords = {multiscale computing; stochastic systems; Fokker-Planck equation; uncertainty propagation},

language = {eng},

number = {3},

pages = {541-561},

publisher = {EDP-Sciences},

title = {An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations},

url = {http://eudml.org/doc/273243},

volume = {45},

year = {2011},

}

TY - JOUR

AU - Frederix, Yves

AU - Samaey, Giovanni

AU - Roose, Dirk

TI - An analysis of noise propagation in the multiscale simulation of coarse Fokker-Planck equations

JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

PY - 2011

PB - EDP-Sciences

VL - 45

IS - 3

SP - 541

EP - 561

AB - We consider multiscale systems for which only a fine-scale model describing the evolution of individuals (atoms, molecules, bacteria, agents) is given, while we are interested in the evolution of the population density on coarse space and time scales. Typically, this evolution is described by a coarse Fokker-Planck equation. In this paper, we consider a numerical procedure to compute the solution of this Fokker-Planck equation directly on the coarse level, based on the estimation of the unknown parameters (drift and diffusion) using only appropriately chosen realizations of the fine-scale, individual-based system. As these parameters might be space- and time-dependent, the estimation is performed in every spatial discretization point and at every time step. If the fine-scale model is stochastic, the estimation procedure introduces noise on the coarse level. We investigate stability conditions for this procedure in the presence of this noise and present an analysis of the propagation of the estimation error in the numerical solution of the coarse Fokker-Planck equation.

LA - eng

KW - multiscale computing; stochastic systems; Fokker-Planck equation; uncertainty propagation

UR - http://eudml.org/doc/273243

ER -

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