• Previous Article
    Oscillatory behavior of Asymptotic-Preserving splitting methods for a linear model of diffusive relaxation
  • KRM Home
  • This Issue
  • Next Article
    On some properties of linear and linearized Boltzmann collision operators for hard spheres
December  2008, 1(4): 557-572. doi: 10.3934/krm.2008.1.557

Derivation of a kinetic model from a stochastic particle system


3-Université de Toulouse (UPS, INSA, UT1, UTM) & CNRS, Institut de Mathématiques de Toulouse (UMR 5219), 118 Route de Narbonne, F-31062 Toulouse, France


TU Kaiserslautern, Department of Mathematics, Postfach 3049, 67653 Kaiserslautern, Germany


Fraunhofer Institute ITWM, Fraunhofer-Platz 1, 67663 Kaiserslautern


University of Durham, School of Engineering, South Road Durham DH1 3LE, United Kingdom


TU Berlin, Department of Mathematics, Straße des 17.Juni 136, 10623 Berlin, Germany

Received  July 2008 Revised  September 2008 Published  October 2008

We study a stochastic lattice particle system with exclusion principle. A kinetic equation and its diffusion limit are formally derived from the Monte Carlo dynamics. This derivation is investigated analytically and numerically and compared with the classical hydrodynamic limit of the stochastic exclusion process. Numerical results are presented for different values of jump probabilities.
Citation: Pierre Degond, Simone Goettlich, Axel Klar, Mohammed Seaid, Andreas Unterreiter. Derivation of a kinetic model from a stochastic particle system. Kinetic and Related Models, 2008, 1 (4) : 557-572. doi: 10.3934/krm.2008.1.557

Zhiyan Ding, Qin Li. Constrained Ensemble Langevin Monte Carlo. Foundations of Data Science, 2022, 4 (1) : 37-70. doi: 10.3934/fods.2021034


Xinping Zhou, Yong Li, Xiaomeng Jiang. Periodic solutions in distribution of stochastic lattice differential equations. Discrete and Continuous Dynamical Systems - B, 2022  doi: 10.3934/dcdsb.2022123


Giacomo Dimarco. The moment guided Monte Carlo method for the Boltzmann equation. Kinetic and Related Models, 2013, 6 (2) : 291-315. doi: 10.3934/krm.2013.6.291


Guillaume Bal, Ian Langmore, Youssef Marzouk. Bayesian inverse problems with Monte Carlo forward models. Inverse Problems and Imaging, 2013, 7 (1) : 81-105. doi: 10.3934/ipi.2013.7.81


Ajay Jasra, Kody J. H. Law, Yaxian Xu. Markov chain simulation for multilevel Monte Carlo. Foundations of Data Science, 2021, 3 (1) : 27-47. doi: 10.3934/fods.2021004


Theodore Papamarkou, Alexey Lindo, Eric B. Ford. Geometric adaptive Monte Carlo in random environment. Foundations of Data Science, 2021, 3 (2) : 201-224. doi: 10.3934/fods.2021014


B. S. Goh, W. J. Leong, Z. Siri. Partial Newton methods for a system of equations. Numerical Algebra, Control and Optimization, 2013, 3 (3) : 463-469. doi: 10.3934/naco.2013.3.463


Cheng-Hsiung Hsu, Jian-Jhong Lin. Stability analysis of traveling wave solutions for lattice reaction-diffusion equations. Discrete and Continuous Dynamical Systems - B, 2020, 25 (5) : 1757-1774. doi: 10.3934/dcdsb.2020001


Cédric Bernardin, Valeria Ricci. A simple particle model for a system of coupled equations with absorbing collision term. Kinetic and Related Models, 2011, 4 (3) : 633-668. doi: 10.3934/krm.2011.4.633


Arnaud Debussche, Julien Vovelle. Diffusion limit for a stochastic kinetic problem. Communications on Pure and Applied Analysis, 2012, 11 (6) : 2305-2326. doi: 10.3934/cpaa.2012.11.2305


Michael B. Giles, Kristian Debrabant, Andreas Rössler. Analysis of multilevel Monte Carlo path simulation using the Milstein discretisation. Discrete and Continuous Dynamical Systems - B, 2019, 24 (8) : 3881-3903. doi: 10.3934/dcdsb.2018335


Jiakou Wang, Margaret J. Slattery, Meghan Henty Hoskins, Shile Liang, Cheng Dong, Qiang Du. Monte carlo simulation of heterotypic cell aggregation in nonlinear shear flow. Mathematical Biosciences & Engineering, 2006, 3 (4) : 683-696. doi: 10.3934/mbe.2006.3.683


Naoufel Ben Abdallah, Antoine Mellet, Marjolaine Puel. Fractional diffusion limit for collisional kinetic equations: A Hilbert expansion approach. Kinetic and Related Models, 2011, 4 (4) : 873-900. doi: 10.3934/krm.2011.4.873


Jean Dolbeault. An introduction to kinetic equations: the Vlasov-Poisson system and the Boltzmann equation. Discrete and Continuous Dynamical Systems, 2002, 8 (2) : 361-380. doi: 10.3934/dcds.2002.8.361


Julian Koellermeier, Roman Pascal Schaerer, Manuel Torrilhon. A framework for hyperbolic approximation of kinetic equations using quadrature-based projection methods. Kinetic and Related Models, 2014, 7 (3) : 531-549. doi: 10.3934/krm.2014.7.531


Piermarco Cannarsa, Giuseppe Da Prato. Invariance for stochastic reaction-diffusion equations. Evolution Equations and Control Theory, 2012, 1 (1) : 43-56. doi: 10.3934/eect.2012.1.43


Wilhelm Stannat, Lukas Wessels. Deterministic control of stochastic reaction-diffusion equations. Evolution Equations and Control Theory, 2021, 10 (4) : 701-722. doi: 10.3934/eect.2020087


Peng Gao. Limiting dynamics for stochastic nonclassical diffusion equations. Discrete and Continuous Dynamical Systems - B, 2021  doi: 10.3934/dcdsb.2021288


Nicolas Fournier. Particle approximation of some Landau equations. Kinetic and Related Models, 2009, 2 (3) : 451-464. doi: 10.3934/krm.2009.2.451


Jean Dolbeault, Giuseppe Toscani. Fast diffusion equations: Matching large time asymptotics by relative entropy methods. Kinetic and Related Models, 2011, 4 (3) : 701-716. doi: 10.3934/krm.2011.4.701

2021 Impact Factor: 1.398


  • PDF downloads (67)
  • HTML views (0)
  • Cited by (1)

[Back to Top]