Open Access
Volume 28, 2024
Page(s) 46 - 61
Published online 22 February 2024
  1. D. Adams, G. dos Reis, R. Ravaille, W. Salkeld and J. Tugaut, Large deviations and exit-times for reflected McKean–Vlasov equations with self-stabilising terms and superlinear drifts. Stochastic Process. Appl. 146 (2022) 264–310. [CrossRef] [MathSciNet] [Google Scholar]
  2. M. Benaïm, M. Ledoux and O. Raimond, Self-interacting diffusions. Probab. Theory Related Fields 122 (2002) 1–41. [CrossRef] [MathSciNet] [Google Scholar]
  3. M. Benaïm and O. Raimond, Self-interacting diffusions. III. Symmetric interactions. Ann. Probab. 33 (2005) 1717–1759. [MathSciNet] [Google Scholar]
  4. S. Benachour, B. Roynette, D. Talay and P. Vallois, Nonlinear self-stabilizing processes. I. Existence, invariant probability, propagation of chaos. Stochastic Process. Appl. 75 (1998) 173–201. [CrossRef] [MathSciNet] [Google Scholar]
  5. P. Cattiaux, A. Guillin and F. Malrieu, Probabilistic approach for granular media equations in the non-uniformly convex case. Probab. Theory Related Fields 140 (2008) 19–40. [CrossRef] [MathSciNet] [Google Scholar]
  6. S. Chambeu and A. Kurtzmann, Some particular self-interacting diffusions: ergodic behaviour and almost sure convergence. Bernoulli 17 (2011) 1248–1267. [CrossRef] [MathSciNet] [Google Scholar]
  7. J.A. Carrillo, R.J. McCann and C. Villani, Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates. Rev. Mat. Iberoamericana 19 (2003) 971–1018. [CrossRef] [MathSciNet] [Google Scholar]
  8. R.T. Durrett and L.C.G. Rogers, Asymptotic behavior of Brownian polymers. Probab. Theory Related Fields 92 (1992) 337–349. [CrossRef] [MathSciNet] [Google Scholar]
  9. A. Dembo and O. Zeitouni, Large deviations techniques and applications, Vol. 38 of Stochastic Modelling and Applied Probability. Springer-Verlag, Berlin (2010). [CrossRef] [Google Scholar]
  10. M.I. Freidlin and A.D. Wentzell, Random perturbations of dynamical systems, Vol. 260 of Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 2nd edn. Springer-Verlag, New York (1998). [CrossRef] [Google Scholar]
  11. S. Herrmann, P. Imkeller and D. Peithmann, Large deviations and a Kramers’ type law for self-stabilizing diffusions. Ann. Appl. Probab. 18 (2008) 1379–1423. [CrossRef] [MathSciNet] [Google Scholar]
  12. S. Herrmann and J. Tugaut, Stationary measures for self-stabilizing processes: asymptotic analysis in the small noise limit. Electron. J. Probab. 15 (2010) 2087–2116. [CrossRef] [MathSciNet] [Google Scholar]
  13. S. Herrmann and J. Tugaut, Self-stabilizing processes: uniqueness problem for stationary measures and convergence rate in the small-noise limit. ESAIM Probab. Stat. 16 (2012) 277–305. [CrossRef] [EDP Sciences] [MathSciNet] [Google Scholar]
  14. S. Jazaerli and Y.F. Saporito, Functional Itô calculus, path-dependence and the computation of Greeks. Stochastic Process. Appl. 127 (2017) 3997–4028. [CrossRef] [MathSciNet] [Google Scholar]
  15. V. Kleptsyn and A. Kurtzmann, Ergodicity of self-attracting motion. Electron. J. Probab. 17 (2012) 37. [CrossRef] [Google Scholar]
  16. A. Kurtzmann, The ODE method for some self-interacting diffusions on Rd. Ann. Inst. Henri Poincaré Probab. Stat. 46 (2010) 618–643. [CrossRef] [MathSciNet] [Google Scholar]
  17. J.R. Norris, L.C.G. Rogers and D. Williams, Self-avoiding random walk: a Brownian motion model with local time drift. Probab. Theory Related Fields 74 (1987) 271–287. [CrossRef] [MathSciNet] [Google Scholar]
  18. O. Raimond, Self-interacting diffusions: a simulated annealing version. Probab. Theory Related Fields 144 (2009) 247–279. [CrossRef] [MathSciNet] [Google Scholar]
  19. L.C.G. Rogers and D. Williams, Diffusions, Markov Processes and Martingales: Itô Calculus, Vol. 2. Cambridge University Press (2000). [Google Scholar]
  20. P. Ren and F.-Y. Wang, Bismut formula for Lions derivative of distribution dependent SDEs and applications. J. Diff. Equ. 267 (2019) 4745–4777. [CrossRef] [Google Scholar]
  21. J. Tugaut, Exit problem of McKean-Vlasov diffusions in convex landscapes. Electron. J. Probab. 17 (2022) 26. [Google Scholar]
  22. J. Tugautm, A simple proof of a Kramers’ type law for self-stabilizing diffusions. Electron. Commun. Probab. 21 (2016) 7. [CrossRef] [Google Scholar]
  23. J. Tugaut, Exit-problem of McKean–Vlasov diffusions in double-well landscape. J. Theoret. Probab. 31 (2018) 1013–1023. [CrossRef] [MathSciNet] [Google Scholar]
  24. J. Tugaut, A simple proof of a Kramers’ type law for self-stabilizing diffusions in double-wells landscape. ALEA Lat. Am. J. Probab. Math. Stat. 16 (2019) 389–398. [CrossRef] [MathSciNet] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.