Uniform in time interacting particle approximations for nonlinear equations of Patlak-Keller-Segel type

DOI10.1214/17-EJP25zbMath1357.60105arXiv1604.08668OpenAlexW2963996213MaRDI QIDQ508461

Wai-Tong Louis Fan, Amarjit Budhiraja

Publication date: 7 February 2017

Published in: Electronic Journal of Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.08668

zbMATH Keywords

chemotaxiskinetic equationsMcKean-Vlasov equationsEuler approximationsgranular media equationsPatlak-Keller-Segel equationsreinforced diffusionsuniform chaos propagationuniform exponential concentration boundsweakly interacting particle systems

Mathematics Subject Classification ID

Interacting random processes; statistical mechanics type models; percolation theory (60K35) Other physical applications of random processes (60K40) Applications of stochastic analysis (to PDEs, etc.) (60H30) Diffusion processes (60J60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) Cell movement (chemotaxis, etc.) (92C17)

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Approximations of McKean-Vlasov stochastic differential equations with irregular coefficients ⋮ Stationarity and uniform in time convergence for the graphon particle system ⋮ Graphon particle system: uniform-in-time concentration bounds ⋮ Hydrodynamic limit of a stochastic model of proliferating cells with chemotaxis ⋮ Particle approximation of the doubly parabolic Keller-Segel equation in the plane ⋮ Mean-field limit of a particle approximation of the one-dimensional parabolic-parabolic Keller-Segel model without smoothing ⋮ Tamed Euler-Maruyama approximation of McKean-Vlasov stochastic differential equations with super-linear drift and Hölder diffusion coefficients

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