EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 32 (2026) ESAIM: COCV, 32 (2026) 14 References
Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 14
Number of page(s) 33
DOI https://doi.org/10.1051/cocv/2026003
Published online 25 February 2026
  1. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen and O. Shochet, Novel type of phase transition in a system of self-driven particles. Phys. Rev. Lett. 75 (1995) 1226–1229. [CrossRef] [MathSciNet] [PubMed] [Google Scholar]
  2. J.-M. Lasry and P.-L. Lions, Mean field games. Jpn. J. Math. 2 (2007) 229–260. [Google Scholar]
  3. F. Delarue, J. Inglis, S. Rubenthaler and E. Tanré, Particle systems with a singular mean-field self-excitation. application to neuronal networks. Stoch. Processes Appl. 125 (2015) 2451–2492. [Google Scholar]
  4. B. Duchet, C. Bick and A. Byrne, Mean-field approximations with adaptive coupling for networks with spike-timing-dependent plasticity. Neural Computat. 35 (2023) 1481–1528. [Google Scholar]
  5. G. Dumont and P. Gabriel, The mean-field equation of a leaky integrate-and-fire neural network: measure solutions and steady states. Nonlinearity 33 (2020) 6381. [Google Scholar]
  6. P. Robert and J. Touboul, On the dynamics of random neuronal networks. J. Statist. Phys. 165 (2016) 545–584. [Google Scholar]
  7. A. Treves, Mean-field analysis of neuronal spike dynamics. Network Computat. Neural Syst. 4 (1983) 259–284. [Google Scholar]
  8. J. Han, Q. Li, et al., A mean-field optimal control formulation of deep learning. Res. Math. Sci. 6 (2019) 1–41. [Google Scholar]
  9. J. Sirignano and K. Spiliopoulos, Mean field analysis of deep neural networks. Math. Oper. Res. 47 (2022) 120–152. [Google Scholar]
  10. P. Cardaliaguet and S. Hadikhanloo, Learning in mean field games: the fictitious play. ESAIM: Control Optim. Calc. Var. 23 (2017) 569–591. [Google Scholar]
  11. H. Pham and X. Wei, Bellman equation and viscosity solutions for mean-field stochastic control problem. ESAIM: Control Optim. Calc. Var. 24 (2018) 437–461. [Google Scholar]
  12. L. Popovic and A. Veber, A spatial measure-valued model for chemical reaction networks in heterogeneous systems. Ann. Appl. Probab. 33 (2023) 3706–3754. [Google Scholar]
  13. M. Morandotti and F. Solombrino, Mean-field analysis of multipopulation dynamics with label switching. SIAM J. Math. Anal. 52 (2020) 1427–1462. [CrossRef] [MathSciNet] [Google Scholar]
  14. S. Almi, M. Morandotti and F. Solombrino, Optimal control problems in transport dynamics with additive noise. J. Differ. Equ. 373 (2023) 1–47. [Google Scholar]
  15. M. Fornasier, S. Lisini, C. Orrieri and G. Savaré, Mean-field optimal control as gamma-limit of finite agent controls. Eur. J. Appl. Math. 30 (2019) 1153–1186. [CrossRef] [Google Scholar]
  16. A. Baldi, Well-posedness and propagation of chaos for multi-agent models with strategies and diffusive effects. Master's thesis, Politecnico di Torino (2023). [Google Scholar]
  17. A. Baldi and M. Morandotti, Well-posedness and propagation of chaos for multi-agent models with strategies and diffusive effects. arXiv preprint arXiv:2507.14058 (2025). [Google Scholar]
  18. L. Ambrosio, M. Fornasier, M. Morandotti and G. Savare, Spatially inhomogeneous evolutionary games. Commun. Pure Appl. Math. 71 (2018) 1353–1402. [Google Scholar]
  19. G. Ascione, D. Castorina and F. Solombrino, Mean-field sparse optimal control of systems with additive white noise. SIAM J. Math. Anal. 55 (2023) 6965–6990. [Google Scholar]
  20. P. Grazieschi, M. Leocata, C. Mascart, J. Chevallier, F. Delarue and E. Tanré, Network of interacting neurons with random synaptic weights. ESAIM: Proc. Surv. 65 (2019) 445–475. [Google Scholar]
  21. O. Faugeras, E. Soret and E. Tanré, Asymptotic behavior of a network of neurons with random linear interactions. arXiv preprint arXiv:2006.03083 (2020). [Google Scholar]
  22. O.D. Faugeras, J.D. Touboul and B. Cessac, A constructive mean-field analysis of multi population neural networks with random synaptic weights and stochastic inputs. Front. Computat. Neurosci. 3 (2009) 323. [Google Scholar]
  23. A. De Masi, A. Galves, E. Löcherbach and E. Presutti, Hydrodynamic limit for interacting neurons. J. Statist. Phys. 158 (2015) 866–902. [CrossRef] [Google Scholar]
  24. N. Fournier and E. Löcherbach, On a toy model of interacting neurons. Ann. Inst. Henri Poincaré Probab. Statist. 52 (2016) 1844–1876. [Google Scholar]
  25. G. La Camera, The mean field approach for populations of spiking neurons, in Computational Modelling of the Brain: Modelling Approaches to Cells, Circuits and Networks. Springer (2021) 125–157. [Google Scholar]
  26. M. Tamborrino and P. Lansky, Shot noise, weak convergence and diffusion approximations. Physica D: Nonlinear Phenomena 418 (2021) 132845. [Google Scholar]
  27. G. Ascione, G. D'Onofrio, L. Kostal and E. Pirozzi, An optimal Gauss-Markov approximation for a process with stochastic drift and applications. Stoch. Processes Appl. 130 (2020) 6481–6514. [Google Scholar]
  28. P.H. Baxendale and P.E. Greenwood, Sustained oscillations for density dependent Markov processes. J. Math. Biol. 63 (2011) 433–457. [Google Scholar]
  29. S. Ditlevsen and P. Greenwood, The Morris-Lecar neuron model embeds a leaky integrate-and-fire model. J. Math. Biol. 67 (2013) 239–259. [Google Scholar]
  30. Q. Cormier, E. Tanré and R. Veltz, Long time behavior of a mean-field model of interacting neurons. Stoch. Processes Appl. 130 (2020) 2553–2595. [Google Scholar]
  31. E. Locherbach, Fluctuations for mean field limits of interacting systems of spiking neurons. Ann. Inst. Henri Poincaré Probab. Statist. 60 (2024) 790–823. [Google Scholar]
  32. G. Ascione and G. D'Onofrio, Deterministic control of SDEs with stochastic drift and multiplicative noise: a variational approach. Appl. Math. Optim. 88 (2023) 11. [Google Scholar]
  33. E. Löcherbach, Spiking neurons: interacting Hawkes processes, mean field limits and oscillations. ESAIM: Proc. Surv. 60 (2017) 90–103. [Google Scholar]
  34. V. Panaretos and Y. Zemel, An Invitation to Statistics in Wasserstein Space. SpringerBriefs in Probability and Mathematical Statistics. Cambridge University Press (2020). [Google Scholar]
  35. R.F. Arens and J. Eells Jr., On embedding uniform and topological spaces. Pacific J. Math. 6 (1956) 397–403. [Google Scholar]
  36. Z.-M. Ma and M. Röckner, Introduction to the Theory of (Non-symmetric) Dirichlet Forms. Springer Science & Business Media (2012). [Google Scholar]
  37. G. Da Prato and J. Zabczyk, Stochastic Equations in Infinite Dimensions, vol. 152. Cambridge University Press (2014). [Google Scholar]
  38. A.-S. Sznitman, Topics in propagation of chaos. Ecole Probab. Saint-Flour XIX 1464 (1991) 165–251. [Google Scholar]
  39. L.-P. Chaintron and A. Diez, Propagation of chaos: a review of models, methods and applications. I. models and methods. Kinetic Related Models 15 (2022) 895. [Google Scholar]
  40. L.-P. Chaintron and A. Diez, Propagation of chaos: a review of models, methods and applications. II. applications. Kinetic Related Models 15 (2022) 1017. [Google Scholar]
  41. P. Billingsley, Convergence of probability measures. Wiley Series in Probability and Statistics: Probability and Statistics, 2nd edn. John Wiley & Sons, Inc., New York (1999). A Wiley-Interscience Publication. [Google Scholar]
  42. A. Dembo and O. Zeitouni, Large Deviations Techniques and Applications. Jones and Bartlett Publishers, Boston, MA (1993). [Google Scholar]
  43. P. Lánskỳ and V. Lanska, Diffusion approximation of the neuronal model with synaptic reversal potentials. Biol. Cybernet. 56 (1987) 19–26. [Google Scholar]
  44. K. Pakdaman, B. Perthame and D. Salort, Dynamics of a structured neuron population. Nonlinearity 23 (2009) 55. [Google Scholar]
  45. J.A Cañizo and H. Yoldaş, Asymptotic behaviour of neuron population models structured by elapsed-time. Nonlinearity 32 (2019) 464. [CrossRef] [MathSciNet] [Google Scholar]
  46. H. Brézis, Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. North-Holland Mathematics Studies. North-Holland, Amsterdam-London; American Elsevier, New York (1973). [Google Scholar]
  47. L. Manca, Kolmogorov operators in spaces of continuous functions and equations for measures. Vol. 10 of Tesi. Scuola Normale Superiore di Pisa (Nuova Series). Edizioni della Normale, Pisa (2008). [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.