Mean Field Control with Absorption

References

• [1] Bayraktar E, Cecchin A, Chakraborty P (2023) Mean field control and finite agent approximation for regime-switching jump diffusions. Appl. Math. Optim. 88(2):36.Crossref, Google Scholar
• [2] Bayraktar E, Ekren I, Zhang X (2025c) Convergence rate of particle system for second-order PDEs on Wasserstein space. SIAM J. Control Optim. 63(3): 1768–1782.Google Scholar
• [3] Bayraktar E, Ekren I, Zhang X (2025b) Comparison of viscosity solutions for a class of second-order PDEs on the Wasserstein space. Comm. Partial Differential Equations 50(4):570–613.Crossref, Google Scholar
• [4] Bayraktar E, Ekren I, He X, Zhang X (2026) Comparison for semi-continuous viscosity solutions for second order PDEs on the Wasserstein space. J. Differential Equations 455:113963.Google Scholar
• [5] Bayraktar E, Cheung H, Ekren I, Qiu J, Tai HM, Zhang X (2025a) Viscosity solutions of fully second-order HJB equations in the Wasserstein space. Preprint, submitted January 3, https://arxiv.org/abs/2501.01612.Google Scholar
• [6] Bertucci C (2023) Stochastic optimal transport and Hamilton-Jacobi-Bellman equations on the set of probability measures. Preprint, submitted June 7, https://arxiv.org/abs/2306.04283v1.Google Scholar
• [7] Bertucci C, Lions PL, Souganidis PE (2026) Optimal control of the Dyson equation and large deviations for Hermitian random matrices. Working paper, Université ParisDauphine, Paris.Google Scholar
• [8] Bogachev VI, Krylov NV, Röckner M, Shaposhnikov SV (2015) Fokker–Planck–Kolmogorov Equations, Mathematical Surveys and Monographs, vol. 207 (American Mathematical Society, Providence, RI).Google Scholar
• [9] Briani A, Cardaliaguet P (2018) Stable solutions in potential mean field game systems. Nonlinear Differential Equations Appl. NoDEA 25:1. Crossref, Google Scholar
• [10] Budhiraja A, Dupuis P, Fischer M (2012) Large deviation properties of weakly interacting processes via weak convergence methods. Ann. Probab. 40(1):74–102.Crossref, Google Scholar
• [11] Burzoni M, Campi L (2023) Mean field games with absorption and common noise with a model of bank run. Stochastic Processes Appl. 164:206–241.Crossref, Google Scholar
• [12] Campi L, Fischer M (2018) N-player games and mean-field games with absorption. Ann. Appl. Probab. 28(4):2188–2242.Crossref, Google Scholar
• [13] Campi L, Ghio M, Livieri G (2021) N-player games and mean-field games with smooth dependence on past absorptions. Ann. Inst. Henri Poincaré Probab. Statist. 57(4):1901–1939.Google Scholar
• [14] Cardaliaguet P, Jackson J, Souganidis PE (2026) Mean field control with stopping. Preprint, submitted March 22, https://arxiv.org/abs/2603.21204.Google Scholar
• [15] Cardaliaguet P, Daudin S, Jackson J, Souganidis PE (2023a) An algebraic convergence rate for the optimal control of McKean-Vlasov dynamics. SIAM J. Control Optim. 61(6):3341–3369.Crossref, Google Scholar
• [16] Cardaliaguet P, Jackson J, Mimikos-Stamatopoulos N, Souganidis PE (2023b) Sharp convergence rates for mean field control in the region of strong regularity. Preprint, submitted December 18, https://arxiv.org/abs/2312.11373.Google Scholar
• [17] Carmona R, Delarue F (2018a) Probabilistic Theory of Mean Field Games with Applications I: Mean Field FBSDEs, Control, and Games, Probability Theory and Stochastic Modelling (Springer International Publishing, Cham, Switzerland).Google Scholar
• [18] Carmona R, Delarue F (2018b) Probabilistic Theory of Mean Field Games with Applications II: Mean Field Games with Common Noise and Master Equations, Probability Theory and Stochastic Modelling (Springer International Publishing, Cham, Switzerland).Crossref, Google Scholar
• [19] Cecchin A, Daudin S, Jackson J, Martini M (2025) Quantitative convergence for mean field control with common noise and degenerate idiosyncratic noise. Electronic J. Probab. 30:1–62.Google Scholar
• [20] Conforti G, Kraaij RC, Tonon D (2023a) Hamilton–Jacobi equations for controlled gradient flows: Cylindrical test functions. Preprint, submitted February 13, https://arxiv.org/abs/2302.06571.Google Scholar
• [21] Conforti G, Kraaij R, Tonon D (2023b) Hamilton–Jacobi equations for controlled gradient flows: The comparison principle. J. Functional Anal. 284(9):109853.Crossref, Google Scholar
• [22] Conforti G, Kraaij RC, Tamanini L, Tonon D (2024) Hamilton–Jacobi equations for Wasserstein controlled gradient flows: Existence of viscosity solutions. Preprint, submitted January 31, https://arxiv.org/abs/2401.02240.Google Scholar
• [23] Daudin S, Seeger B (2024) A comparison principle for semilinear Hamilton-Jacobi-Bellman equations in the Wasserstein space. Calculus Variations Partial Differential Equations 63:106. Crossref, Google Scholar
• [24] Daudin S, Delarue F, Jackson J (2024) On the optimal rate for the convergence problem in mean field control. J. Functional Anal. 287(12):110660.Crossref, Google Scholar
• [25] Daudin S, Jackson J, Seeger B (2025) Well-posedness of Hamilton-Jacobi equations in the Wasserstein space: Non-convex Hamiltonians and common noise. Comm. Partial Differential Equations 50(1–2):1–52.Crossref, Google Scholar
• [26] Djete MF (2022) Extended mean field control problem: A propagation of chaos result. Electronic J. Probab. 27:1–53.Crossref, Google Scholar
• [27] Djete MF, Possamaï D, Tan X (2022) McKean-Vlasov optimal control: Limit theory and equivalence between different formulations. Math. Oper. Res. 47(4):2891–2930. Link, Google Scholar
• [28] Furoto Y, Iwabuchi T (2026) Higher-order derivative estimates for the heat equation on a smooth domain. Comm. Pure Appl. Anal.Google Scholar
• [29] Gangbo W, Mayorga S, Świech A (2021) Finite dimensional approximations of Hamilton-Jacobi-Bellman equations in spaces of probability measures. SIAM J. Math. Anal. 53(2):1320–1356. Crossref, Google Scholar
• [30] Graber PJ, Sircar R (2023) Master equation for Cournot mean field games of control with absorption. J. Differential Equations 343:816–909.Crossref, Google Scholar
• [31] Guo G, Tomasevic M (2024) Mean-field limit of particle systems with absorption. Preprint, submitted July 25, https://arxiv.org/abs/2310.10742v2.Google Scholar
• [32] Hambly B, Ledger S (2017) A stochastic McKean–Vlasov equation for absorbing diffusions on the half-line. Ann. Appl. Probab. 27(5):2698–2752.Crossref, Google Scholar
• [33] Hambly B, Ledger S, Søjmark A (2019) A McKean–Vlasov equation with positive feedback and blow-ups. Ann. Appl. Probab. 29(4):2338–2373.Crossref, Google Scholar
• [34] Lacker D (2017) Limit theory for controlled McKean-Vlasov dynamics. SIAM J. Control Optim. 55:1641–1672.Crossref, Google Scholar
• [35] Ledger S, Søjmark A (2021) At the mercy of the common noise: Blow-ups in a conditional McKean–Vlasov problem. Electronic J. Probab. 26:1–39.Crossref, Google Scholar
• [36] Lions PL (2024) Cours au Collège de France. Accessed January, 2025, https://www.college-de-france.fr/en/agenda/lecture/stochastic-control-with-unknowns.Google Scholar
• [37] Mayorga S, Świech A (2023) Finite dimensional approximations of Hamilton–Jacobi–Bellman equations for stochastic particle systems with common noise. SIAM J. Control Optim. 61(2):820–851. Crossref, Google Scholar
• [38] Nadtochiy S, Shkolnikov M (2019) Particle systems with singular interaction through hitting times: Application in systemic risk modeling. Ann. Appl. Probab. 29(1):89–129.Crossref, Google Scholar
• [39] Nadtochiy S, Shkolnikov M (2020) Mean field systems on networks, with singular interaction through hitting times. Ann. Probab. 48:1520–1556. Crossref, Google Scholar
• [40] Soner HM, Yan Q (2024a) Viscosity solutions of the Eikonal equation on the Wasserstein space. Appl. Math. Optim. 90:1.Crossref, Google Scholar
• [41] Soner HM, Yan Q (2024b) Viscosity solutions for McKean–Vlasov control on a torus. SIAM J. Control Optim. 62(2):903–923.Crossref, Google Scholar
• [42] Waters G, Wang L (2006) w2,p estimates of the heat equation in ω⊂Rn and the restrictions on ∂ω. Math. Methods Appl. Sci. 29(2):123–156.Crossref, Google Scholar
• [43] Ye H, Gao J, Ding Y (2007) A generalized Gronwall inequality and its application to a fractional differential equation. J. Math. Anal. Appl. 328(2):1075–1081.Crossref, Google Scholar
• [44] Zhou J, Touzi N, Zhang J (2024) Viscosity solutions for HJB equations on the process space: Application to mean field control with common noise. Preprint, submitted January 10, https://arxiv.org/abs/2401.04920v1.Google Scholar