K. Abraham R. Nickl On statistical Calderón problems Math. Stat. Learn. 2 2 165 216 10.4171/msl/14
C. Amorino A. Heidari V. Pilipauskaitė M. Podolskij Parameter estimation of discretely observed interacting particle systems Stoch. Processes Their Appl. 163 350 386 4612302 10.1016/j.spa.2023.06.011
J. Baladron D. Fasoli O. Faugeras J. Touboul Mean-field description and propagation of chaos in networks of Hodgkin-Huxley and FitzHugh-Nagumo neurons J. Math. Neurosci. 2 1 50 2927775 10.1186/2190-8567-2-10
D. Belomestny A. Goldenshluger Density deconvolution under general assumptions on the distribution of measurament errors Ann. Stat. 49 2 615 649 10.1214/20-AOS1969
D. Belomestny V. Pilipauskaitė M. Podolskij Semiparametric estimation of McKean-Vlasov SDEs Ann. Inst. Henri Poincaré Probab. Stat. 59 1 79 96 4533721 10.1214/22-AIHP1261
S. Benachour B. Roynette D. Talay P. Vallois Nonlinear self-stabilizing processes, I Existence, invariant probability, propagation of chaos Stoch. processes Their Appl. 75 2 173 201 1632193 10.1016/S0304-4149(98)00018-0
M. Bertero P. Boccacci Introduction to Inverse Problems in Imaging Taylor & Francis 10.1887/0750304359
N.G. de Bruijn The roots of trigonometric integrals Duke Math. J. 17 3 197 226 37351 10.1215/S0012-7094-50-01720-0
D.L. Burkholder E. Pardoux A.S. Sznitman Ecole dété de probabilités de Saint-Flour XIX-1989 Springer
C. Canuto F. Fagnani P. Tilli An Eulerian approach to the analysis of Krause’s consensus models SIAM J. Control. Optim. 50 1 243 265 2888264 10.1137/100793177
J.A. Carrillo R.J. McCann C. Villani Kinetic equilibration rates for granular media and related equations: entropy dissipation and mass transportation estimates Rev. Mat. Iberoam. 19 3 971 1018 2053570 10.4171/rmi/376
P. Cardaliaguet F. Delarue J.M. Lasry P.L. Lions The Master Equation and the Convergence Problem in Mean Field Games (AMS-201) Princeton University Press 10.23943/princeton/9780691190716.001.0001 201
P. Cattiaux A. Guillin F. Malrieu Probabilistic approach for granular media equations in the non-uniformly convex case Probab. Theory Relat. Fields 140 19 40 2357669 10.1007/s00440-007-0056-3
B. Chazelle Q. Jiu Q. Li C. Wang Well-posedness of the limiting equation of a noisy consensus model in opinion dynamics J. Differ. Equ. 263 1 365 397 3631310 10.1016/j.jde.2017.02.036
X. Chen Maximum likelihood estimation of potential energy in interacting particle systems from single-trajectory data Electron. Commun. Probab. 26 1 13 4284626 10.1214/21-ECP416
Comte, F., Genon-Catalot, V.: Nonparametric adaptive estimation for interacting particle systems. Scand. J. Stat. (2023)
N.G. de Bruijn The roots of trigonometric integrals Duke Math. J. 17 3 197 226 37351 10.1215/S0012-7094-50-01720-0
L. Della Maestra M. Hoffmann Nonparametric estimation for interacting particle systems: McKean-Vlasov models Probab. Theory Relat. Fields 182 551 613 4367954 10.1007/s00440-021-01044-6
L. Della Maestra M. Hoffmann The LAN property for McKean-Vlasov models in a mean-field regime Stoch. Processes Their Appl. 155 109 146 4503434 10.1016/j.spa.2022.10.002
B. Djehiche F. Gozzi G. Zanco M. Zanella Optimal portfolio choice with path dependent benchmarked labor income: a mean field model Stoch. Processes Their Appl. 145 48 85 4356684 10.1016/j.spa.2021.11.010
G. Doetsch Introduction to the Theory and Application of the Laplace Transformation Springer
Dupuy, T.: Hadamard theorem and entire functions of finite order—for Math 331. Lecture notes. https://tdupu.github.io/complexspring2017/hadamard.pdf (2017)
V. Genon-Catalot C. Laredo Probabilistic properties and parametric inference of small variance nonlinear self-stabilizing stochastic differential equations Stoch. Processes Their Appl. 142 513 548 4324348 10.1016/j.spa.2021.09.002
V. Genon-Catalot C. Laredo Parametric inference for small variance and long time horizon McKean-Vlasov diffusion models Electron. J. Stat. 15 2 5811 5854 4355698 10.1214/21-EJS1922
Genon-Catalot, V., Laredo, C.: Inference for ergodic McKean-Vlasov stochastic differential equations with polynomial interactions. Annales de l’Institut Henri Poincaré, Probabilités et Statistiques. Preprint hal-03866218 (2023)
K. Giesecke G. Schwenkler J. Sirignano Inference for large financial systems Math. Financ. 30 1 3 46 4067069 10.1111/mafi.12222
Guyon, J., Henry-Labordere, P.: The smile calibration problem solved. Available at SSRN 1885032 (2011)
G.H. Hardy A theorem concerning Fourier transforms J. Lond. Math. Soc. 1 3 227 231 1574130 10.1112/jlms/s1-8.3.227
M. Hoffmann A. Olivier Nonparametric estimation of the division rate of an age dependent branching process Stoch. Processes Their Appl. 126 5 1433 1471 3473101 10.1016/j.spa.2015.11.009
A.S. Holland Introduction to the Theory of Entire Functions Academic Press
Huo, X., Zhan, Y.: A note on the entire functions: theorems, properties and examples. In: Journal of Physics: Conference Series, vol. 2012, no. 1, p. 012058. IOP Publishing (2021)
J. Johannes Deconvolution with unknown error distribution Ann. Stat. 37 5A 2301 2323 2543693 10.1214/08-AOS652
B. Jourdain S. Méléard Propagation of chaos and fluctuations for a moderate model with smooth initial data Annales de l’Institut Henri Poincaré (B) Probability and Statistics 34 6 727 766 1653393 10.1016/S0246-0203(99)80002-8
I.P. Kamynin Generalization of the theorem of Marcinkiewicz on entire characteristic functions of probability distributions J. Sov. Math. 20 3 2175 2180 10.1007/BF01239994
R.A. Kasonga Maximum likelihood theory for large interacting systems SIAM J. Appl. Math. 50 3 865 875 1050917 10.1137/0150050
B.Y. Levin Lectures on Entire Functions Providence American Mathematical Society
Linnik, Y.V., Ostrovskii, I.V.: Decomposition of random variables and vectors. AMS 48 (1977)
M. Maïda T.D. Nguyen T.M. Pham Ngoc V. Rivoirard V.C. Tran Statistical deconvolution of the free Fokker-Planck equation at fixed time Bernoulli 28 2 771 802 4388919 10.3150/21-BEJ1366
F. Malrieu Logarithmic Sobolev inequalities for some nonlinear PDE’s Stoch. Processes Their Appl. 95 1 109 132 1847094 10.1016/S0304-4149(01)00095-3
F. Malrieu Convergence to equilibrium for granular media equations and their Euler schemes Ann. Appl. Probab. 13 2 540 560 1970276 10.1214/aoap/1050689593
H.P. McKean Jr A class of Markov processes associated with nonlinear parabolic equations Proc. Natl. Acad. Sci. 56 6 1907 1911 221595 10.1073/pnas.56.6.1907
Méléard, S.: Asymptotic behaviour of some interacting particle systems; McKean-Vlasov and Boltzmann models. In: Probabilistic Models for Nonlinear Partial Differential Equations, Lecture Notes in Mathematics, 1627, pp. 42–95. Springer (1996)
A. Mogilner L. Edelstein-Keshet A non-local model for a swarm J. Math. Biol. 38 534 570 1698215 10.1007/s002850050158
F. Monard R. Nickl G.P. Paternain consistent inversion of noisy non-Abelian X-ray transforms Commun. Pure Appl. Math. 74 5 1045 1099 4230066 10.1002/cpa.21942
R. Nickl Bernstein von Mises theorems for statistical inverse problems I: Schrödinger equation J. Eur. Math. Soc. 22 8 2697 2750 4118619 10.4171/jems/975
G.A. Pavliotis A. Zanoni Eigenfunction martingale estimators for interacting particle systems and their mean field limit SIAM J. Appl. Dyn. Syst. 21 4 2338 2370 4513316 10.1137/21M1464348
Pavliotis, G.A., Zanoni, A.: A method of moments estimator for interacting particle systems and their mean field limit. Preprint arXiv:2212.00403 (2022)
A.M. Sedletskii Classes of entire functions that are rapidly decreasing on the real axis: theory and applications Sb. Math. 199 1 131 2410149 10.1070/SM2008v199n01ABEH003913
E. Seneta Regularly Varying Functions Springer 508
L. Sharrock N. Kantas P. Parpas G.A. Pavliotis Online parameter estimation for the McKean-Vlasov stochastic differential equation Stoch. Processes Their Appl. 162 481 546 4597535 10.1016/j.spa.2023.05.002
A.B. Tsybakov Introduction to Nonparametric Estimation New York Springer 10.1007/b13794
D.V. Widder The Laplace Transformation Princeton University Press
