Large deviations and a Kramers' type law for self-stabilizing diffusions

DOI10.1214/07-AAP489zbMath1149.60020arXivmath/0605053OpenAlexW2030918716MaRDI QIDQ939074

Dierk Peithmann, Peter Imkeller, Samuel Herrmann

Publication date: 20 August 2008

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605053

zbMATH Keywords

diffusionlarge deviationsdomain of attractionexit timeinteracting particle systemspropagation of chaosSelf-stabilizationexit law

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Interacting particle systems in time-dependent statistical mechanics (82C22) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Large deviations (60F10) Generation, random and stochastic difference and differential equations (37H10)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Quantitative concentration inequalities for empirical measures on non-compact spaces
• Logarithmic Sobolev inequalities for some nonlinear PDE's.
• Nonlinear self-stabilizing processes. I: Existence, invariant probability, propagation of chaos
• Nonlinear self-stabilizing processes. II: Convergence to invariant probability
• A certain class of diffusion processes associated with nonlinear parabolic equations
• A law of large numbers for moderately interacting diffusion processes
• Recent progress on the small parameter exit problem^†
• Asymptotic Exit Time Distributions
• Large deviations from the mckean-vlasov limit for weakly interacting diffusions
• On the exponential exit law in the small parameter exit problem
• A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS

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