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January 2003 A stochastic particle method with random weights for the computation of statistical solutions of McKean-Vlasov equations
Denis Talay, Olivier Vaillant
Ann. Appl. Probab. 13(1): 140-180 (January 2003). DOI: 10.1214/aoap/1042765665

Abstract

We are interested in statistical solutions of McKean-Vlasov-Fokker-Planck equations. An example of motivation is the Navier-Stokes equation for the vorticity of a two-dimensional incompressible fluid flow. We propose an original and efficient numerical method to compute moments of such solutions. It is a stochastic particle method with random weights. These weights are defined through nonparametric estimators of a regression function and convey the uncertainty on the initial condition of the considered equation. We prove an existence and uniqueness result for a class of nonlinear stochastic differential equations (SDEs), and we study the relationship between these nonlinear SDEs and statistical solutions of the corresponding McKean-Vlasov equations. This result forms the foundation of our stochastic particle method where we estimate the convergence rate in terms of the numerical parameters: the number of simulated particles and the time discretization step.

Citation

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Denis Talay. Olivier Vaillant. "A stochastic particle method with random weights for the computation of statistical solutions of McKean-Vlasov equations." Ann. Appl. Probab. 13 (1) 140 - 180, January 2003. https://doi.org/10.1214/aoap/1042765665

Information

Published: January 2003
First available in Project Euclid: 16 January 2003

zbMATH: 1026.60110
MathSciNet: MR1951996
Digital Object Identifier: 10.1214/aoap/1042765665

Subjects:
Primary: 60K35
Secondary: 65C20 , 65U05

Keywords: McKean-Vlasov equation , statistical solution , Stochastic particle methods

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.13 • No. 1 • January 2003
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