Electronic Journal of Probability

Exit problem of McKean-Vlasov diffusions in convex landscapes

Julian Tugaut

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The exit time and the exit location of a non-Markovian diffusion is analyzed. More particularly, we focus on the so-called self-stabilizing process. The question has been studied by Herrmann, Imkeller and Peithmann (in 2008) with results similar to those by Freidlin and Wentzell. We aim to provide the same results by a more intuitive approach and without reconstructing the proofs of Freidlin and Wentzell. Our arguments are as follows. In one hand, we establish a strong version of the propagation of chaos which allows to link the exit time of the McKean-Vlasov diffusion and the one of a particle in a mean-field system. In the other hand, we apply the Freidlin-Wentzell theory to the associated mean field system, which is a Markovian diffusion.

Article information

Electron. J. Probab., Volume 17 (2012), paper no. 76, 26 pp.

Accepted: 12 September 2012
First available in Project Euclid: 4 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60F10: Large deviations
Secondary: 60J60: Diffusion processes [See also 58J65] 60H10: Stochastic ordinary differential equations [See also 34F05] 82C22: Interacting particle systems [See also 60K35]

Self-stabilizing diffusion Exit time Exit location Large deviations Interacting particle systems Propagation of chaos Granular media equation

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Tugaut, Julian. Exit problem of McKean-Vlasov diffusions in convex landscapes. Electron. J. Probab. 17 (2012), paper no. 76, 26 pp. doi:10.1214/EJP.v17-1914. https://projecteuclid.org/euclid.ejp/1465062398

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