F. Baccelli, D. Hong and Z. Liu. Fixed point methods for the simulation of the sharing of a local loop by a large number of interacting TCP connections. Technical report 4154, INRIA, 2001.
D. Belomestny and J. Schoenmakers. Projected particle methods for solving McKean–Vlasov stochastic differential equations. SIAM J. Numer. Anal. 56 (6) (2018) 3169–3195. MR3871063 https://doi.org/10.1137/17M1111024
S. Benachour, B. Roynette, D. Talay and P. Vallois. Nonlinear self-stabilizing processes – I Existence, invariant probability, propagation of chaos. Stochastic Process. Appl. 75 (2) (1998) 173–201. MR1632193 https://doi.org/10.1016/S0304-4149(98)00018-0
J. P. N. Bishwal. Estimation in interacting diffusions: Continuous and discrete sampling. Appl. Math. 2 (9) (2011) 1154–1158. MR2924983 https://doi.org/10.4236/am.2011.29160
P. Cattiaux, A. Guillin and F. Malrieu. Probabilistic approach for granular media equations in the non-uniformly convex case. Probab. Theory Related Fields 140 (1–2) (2008) 19–40. MR2357669 https://doi.org/10.1007/s00440-007-0056-3
J. Chang and S. X. Chen. On the approximate maximum likelihood estimation for diffusion processes. Ann. Statist. 39 (6) (2011) 2820–2851. MR3012393 https://doi.org/10.1214/11-AOS922
G. Ciołek, D. Marushkevych and M. Podolskij. On Dantzig and Lasso estimators of the drift in a high dimensional Ornstein–Uhlenbeck model. Electron. J. Stat. 14 (2) (2020) 4395–4420. MR4194266 https://doi.org/10.1214/20-EJS1775
L. Della Maestra and M. Hoffmann. Nonparametric estimation for interacting particle systems: McKean–Vlasov models. Probab. Theory Related Fields (2021). https://doi.org/10.1007/s00440-021-01044-6
J.-P. Fouque and Z. Zhang. Deep learning methods for mean field control problems with delay. Frontiers in Applied Mathematics and Statistics 6 (11) (2020).
T. D. Frank. Nonlinear Fokker–Planck Equations: Fundamentals and Applications. Springer Science & Business Media, 2005. MR2118870
S. Gaïffas and G. Matulewicz. Sparse inference of the drift of a high-dimensional Ornstein–Uhlenbeck process. J. Multivariate Anal. 169 (2019) 1–20. MR3875583 https://doi.org/10.1016/j.jmva.2018.08.005
V. Genon-Catalot and C. Larédo Parametric inference for small variance and long time horizon McKean–Vlasov diffusion models, 2021. hal-03095560.
V. Genon-Catalot and C. Larédo. Probabilistic properties and parametric inference of small variance nonlinear self-stabilizing stochastic differential equations. Stochastic Process. Appl. 142 (2021) 513–548. MR4324348 https://doi.org/10.1016/j.spa.2021.09.002
K. Giesecke, G. Schwenkler and J. A. Sirignano. Inference for large financial systems. Math. Finance 30 (1) (2020) 3–46. MR4067069 https://doi.org/10.1111/mafi.12222
A. Haurie and P. Marcotte. On the relationship between Nash–Cournot and Wardrop equilibria. Networks 15 (3) (1985) 295–308. MR0801491 https://doi.org/10.1002/net.3230150303
M. Huang, P. E. Caines and R. P. Malhamé. Individual and mass behaviour in large population stochastic wireless power control problems: Centralized and Nash equilibrium solutions. In 42nd IEEE International Conference on Decision and Control (IEEE Cat. No. 03CH37475) 98–103, 1, 2003. IEEE.
R. A. Kasonga. Maximum likelihood theory for large interacting systems. SIAM J. Appl. Math. 50 (3) (1990) 865–875. MR1050917 https://doi.org/10.1137/0150050
V. N. Kolokoltsov. Nonlinear Markov Processes and Kinetic Equations, 182. Cambridge University Press, Cambridge, 2010. MR2680971 https://doi.org/10.1017/CBO9780511760303
Y. A. Kutoyants. Statistical Inference for Ergodic Diffusion Processes. 2013. MR2144185 https://doi.org/10.1007/978-1-4471-3866-2
V. E. Lambson. Self-enforcing collusion in large dynamic markets. J. Econom. Theory 34 (2) (1984) 282–291. MR0771005 https://doi.org/10.1016/0022-0531(84)90145-5
F. Malrieu. Convergence to equilibrium for granular media equations and their Euler schemes. Ann. Appl. Probab. 13 (2) (2003) 540–560. MR1970276 https://doi.org/10.1214/aoap/1050689593
C. Marchioro and M. Pulvirenti. Mathematical Theory of Incompressible Nonviscous Fluids, 96. Springer Science & Business Media, 2012. MR1245492 https://doi.org/10.1007/978-1-4612-4284-0
H. P. McKean. A class of Markov processes associated with nonlinear parabolic equations. Proc. Natl. Acad. Sci. USA 56 (6) (1966) 1907–1911. MR0221595 https://doi.org/10.1073/pnas.56.6.1907
J. M. McNamara, A. I. Houston and E. J. Collins. Optimality models in behavioral biology. SIAM Rev. 43 (3) (2001) 413–466. MR1872385 https://doi.org/10.1137/S0036144500385263
A. Meister. Deconvolution Problems in Nonparametric Statistics. Lecture Notes in Statistics, 2009. MR2768576 https://doi.org/10.1007/978-3-540-87557-4
R. Nickl and J. Söhl. Nonparametric Bayesian posterior contraction rates for discretely observed scalar diffusions. Ann. Statist. 45 (4) (2017) 1664–1693. MR3670192 https://doi.org/10.1214/16-AOS1504
P. Ren and J.-L. Wu. Least squares estimator for path-dependent McKean–Vlasov SDEs via discrete-time observations. Acta Math. Sci. 39B (3) (2019) 691–716. MR4066500 https://doi.org/10.1007/s10473-019-0305-4
L. Sharrock, N. Kantas, P. Parpas and G. A. Pavliotis Parameter estimation for the McKean–Vlasov stochastic differential equation, 2021. Available at arXiv:2106.13751v2 [math.ST]
C. Strauch. Adaptive invariant density estimation for ergodic diffusions over anisotropic classes. Ann. Statist. 46 (6B) (2018) 3451–3480. MR3852658 https://doi.org/10.1214/17-AOS1664
A.-S. Sznitman. Topics in propagation of chaos. In Ecole D’été de Probabilités de Saint-Flour XIX–1989 165–251. Springer, Berlin, 1991. MR1108185 https://doi.org/10.1007/BFb0085169
A. B. Tsybakov. Introduction to Nonparametric Estimation. Springer Series in Statistics, 2009. MR2724359 https://doi.org/10.1007/b13794
