Self-stabilizing processes in multi-wells landscape in \(\mathbb{R}^d\)-invariant probabilities

DOI10.1007/s10959-012-0435-2zbMath1314.60119OpenAlexW1967761535MaRDI QIDQ457091

Julian Tugaut

Publication date: 26 September 2014

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

Full work available at URL: https://doi.org/10.1007/s10959-012-0435-2

zbMATH Keywords

uniqueness problemstationary measuresgranular media equationfree-energyMcKean-Vlasov stochastic differential equationsself-interacting diffusion

Mathematics Subject Classification ID

Stationary stochastic processes (60G10) Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Nonlinear parabolic equations (35K55) Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Diffusion processes (60J60)

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Cites Work

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• Convergence to the equilibria for self-stabilizing processes in double-well landscape
• Stationary measures for self-stabilizing processes: asymptotic analysis in the small noise limit
• McKean-Vlasov diffusions: from the asynchronization to the synchronization
• Large deviations and a Kramers' type law for self-stabilizing diffusions
• Non-uniqueness of stationary measures for self-stabilizing processes
• Increasing propagation of chaos for mean field models
• A non-Maxwellian steady distribution for one-dimensional granular media
• Convergence to equilibrium for granular media equations and their Euler schemes
• Nonlinear self-stabilizing processes. I: Existence, invariant probability, propagation of chaos
• Nonlinear self-stabilizing processes. II: Convergence to invariant probability
• Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates
• Probabilistic approach for granular media equations in the non-uniformly convex case
• A certain class of diffusion processes associated with nonlinear parabolic equations
• On uniqueness of invariant measures for finite- and infinite-dimensional diffusions
• A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS