Empirical measure and small noise asymptotics under large deviation scaling for interacting diffusions

DOI10.1007/s10959-020-01071-4zbMath1484.60028arXiv1907.07276OpenAlexW3120386494MaRDI QIDQ2116481

Amarjit Budhiraja, Michael Conroy

Publication date: 17 March 2022

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

Full work available at URL: https://arxiv.org/abs/1907.07276

zbMATH Keywords

large deviation principleweakly interacting diffusionsFeynman-Kac functionalsFreidlin-Wentzell asymptoticscontrolled McKean-Vlasov equationscontrolled nonlinear Markov processesmean field stochastic control problemsmean field systems with common noise

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Interacting random processes; statistical mechanics type models; percolation theory (60K35) Optimal stochastic control (93E20) Large deviations (60F10) Convergence of probability measures (60B10)

Related Items (4)

Large deviations of Kac's conservative particle system and energy nonconserving solutions to the Boltzmann equation: a counterexample to the predicted rate function ⋮ Importance sampling for the empirical measure of weakly interacting diffusions ⋮ Large deviations for interacting multiscale particle systems ⋮ Asymptotic behavior of stochastic currents under large deviation scaling with mean field interaction and vanishing noise

Cites Work

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• Large deviations for multiscale diffusion via weak convergence methods
• Large deviation properties of weakly interacting processes via weak convergence methods
• A martingale approach to the law of large numbers for weakly interacting stochastic processes
• Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated
• The Vlasov dynamics and its fluctuations in the \(1/N\) limit of interacting classical particles
• A variational representation for certain functionals of Brownian motion
• Stochastic particle approximations for generalized Boltzmann models and convergence estimates
• Particle representations for a class of nonlinear SPDEs
• A particle system in interaction with a rapidly varying environment: mean field limits and applications
• Default clustering in large portfolios: typical events
• Large deviations for interacting particle systems: joint mean-field and small-noise limit
• Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons
• Large deviations and averaging for systems of slow-fast stochastic reaction-diffusion equations
• Stochastic networks with multiple stable points
• Large Deviations for a Mean Field Model of Systemic Risk
• THE BOUNDED CONFIDENCE MODEL OF OPINION DYNAMICS
• A Multi-Class Mean-Field Model with Graph Structure for TCP Flows
• Central limit theorem for a system of Markovian particles with mean field interactions
• Large deviations from the mckean-vlasov limit for weakly interacting diffusions
• A CLASS OF MARKOV PROCESSES ASSOCIATED WITH NONLINEAR PARABOLIC EQUATIONS

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