Diffusions with a nonlinear irregular drift coefficient and probabilistic interpretation of generalized burgers' equations
B. Jourdain (1997)
ESAIM: Probability and Statistics
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B. Jourdain (1997)
ESAIM: Probability and Statistics
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Hélène Guérin (2004)
ESAIM: Probability and Statistics
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Using probabilistic tools, this work states a pointwise convergence of function solutions of the 2-dimensional Boltzmann equation to the function solution of the Landau equation for Maxwellian molecules when the collisions become grazing. To this aim, we use the results of Fournier (2000) on the Malliavin calculus for the Boltzmann equation. Moreover, using the particle system introduced by Guérin and Méléard (2003), some simulations of the solution of the Landau equation will be given....
Dawson, Donald A., Greven, Andreas (1999)
Electronic Journal of Probability [electronic only]
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Sylvie Meleard (2010)
ESAIM: Probability and Statistics
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This paper gives an approximation of the solution of the Boltzmann equation by stochastic interacting particle systems in a case of cut-off collision operator and small initial data. In this case, following the ideas of Mischler and Perthame, we prove the existence and uniqueness of the solution of this equation and also the existence and uniqueness of the solution of the associated nonlinear martingale problem. Then, we first delocalize the interaction by considering a mollified...
Pierre Del Moral, Laurent Miclo (2000)
Séminaire de probabilités de Strasbourg
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Dawson, Donald A., Li, Zenghu, Wang, Hao (2001)
Electronic Journal of Probability [electronic only]
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Pierre Del Moral, L. Miclo (2003)
ESAIM: Probability and Statistics
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We present an interacting particle system methodology for the numerical solving of the Lyapunov exponent of Feynman–Kac semigroups and for estimating the principal eigenvalue of Schrödinger generators. The continuous or discrete time models studied in this work consists of interacting particles evolving in an environment with soft obstacles related to a potential function . These models are related to genetic algorithms and Moran type particle schemes. Their choice is not unique....
Benjamin Jourdain, Tony Lelièvre, Raphaël Roux (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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We study a free energy computation procedure, introduced in [Darve and Pohorille, (2001) 9169–9183; Hénin and Chipot, (2004) 2904–2914], which relies on the long-time behavior of a nonlinear stochastic differential equation. This nonlinearity comes from a conditional expectation computed with respect to one coordinate of the solution. The long-time convergence of the solutions to this equation has been proved in [Lelièvre , (2008)...
Evans, Steven N., Perkins, Edwin A. (1998)
Electronic Journal of Probability [electronic only]
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Lyne, Owen D., Williams, David (2001)
Electronic Journal of Probability [electronic only]
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Liptser, R., Spokoiny, V. (1999)
Electronic Journal of Probability [electronic only]
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