Stationary measures for self-stabilizing processes: asymptotic analysis in the small noise limit

DOI10.1214/EJP.V15-842zbMath1225.60095MaRDI QIDQ638367

Samuel Herrmann, Julian Tugaut

Publication date: 9 September 2011

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

Full work available at URL: http://www.emis.de/journals/EJP-ECP/_ejpecp/viewarticlecfe4.html

zbMATH Keywords

double well potentialstationary measuresLaplace's methodperturbed dynamical systemself-interacting diffusion

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Diffusion processes (60J60)

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Captivity of the solution to the granular media equation ⋮ Convergence to the equilibria for self-stabilizing processes in double-well landscape ⋮ Stationary solutions of the Vlasov-Fokker-Planck equation: existence, characterization and phase-transition ⋮ Existence and non-uniqueness of stationary distributions for distribution dependent SDEs ⋮ McKean-Vlasov diffusions: from the asynchronization to the synchronization ⋮ Self-stabilizing processes in multi-wells landscape in \(\mathbb{R}^d\)-invariant probabilities ⋮ The Vlasov-Fokker-Planck equation in non-convex landscapes: convergence to equilibrium ⋮ Unnamed Item ⋮ Finiteness of entropy for granular media equations ⋮ A variational approach to nonlinear and interacting diffusions ⋮ Phase transitions of McKean–Vlasov processes in double-wells landscape

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