메뉴 건너뛰기




Volumn 37, Issue 5, 2020, Pages 1211-1244

Fokker-Planck equations of jumping particles and mean field games of impulse control

Author keywords

Fokker Planck equations; Impulse control; Mean field games; Partial differential equations

Indexed keywords

DENSITY OF PARTICLES; IMPULSE CONTROL; IMPULSE CONTROL PROBLEM; MEAN FIELD GAMES; OPTIMAL POLICIES;

EID: 85084698838     PISSN: 02941449     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.anihpc.2020.04.006     Document Type: Article
Times cited : (28)

References (33)
  • 1
    • 77956048120 scopus 로고    scopus 로고
    • Mean field games: numerical methods
    • Achdou, Yves, Capuzzo-Dolcetta, Italo, Mean field games: numerical methods. SIAM J. Numer. Anal. 48:3 (2010), 1136–1162.
    • (2010) SIAM J. Numer. Anal. , vol.48 , Issue.3 , pp. 1136-1162
    • Achdou, Y.1    Capuzzo-Dolcetta, I.2
  • 2
    • 84995814767 scopus 로고    scopus 로고
    • A long-term mathematical model for mining industries
    • Achdou, Yves, Giraud, Pierre-Noel, Lasry, Jean-Michel, Lions, Pierre-Louis, A long-term mathematical model for mining industries. Appl. Math. Optim. 74:3 (2016), 579–618.
    • (2016) Appl. Math. Optim. , vol.74 , Issue.3 , pp. 579-618
    • Achdou, Y.1    Giraud, P.-N.2    Lasry, J.-M.3    Lions, P.-L.4
  • 3
    • 85064459331 scopus 로고    scopus 로고
    • Nonzero-sum stochastic games with impulse controls
    • arXiv preprint
    • Basei, Matteo, Cao, Haoyang, Guo, Xin, Nonzero-sum stochastic games with impulse controls. arXiv preprint arXiv:1901.08085, 2019.
    • (2019)
    • Basei, M.1    Cao, H.2    Guo, X.3
  • 4
    • 0003955188 scopus 로고
    • Impulse Control and Quasi-Variational Inequalities
    • Gaunthier-Villars
    • Bensoussan, Alain, Lions, Jacques Louis, Impulse Control and Quasi-Variational Inequalities. 1984, Gaunthier-Villars.
    • (1984)
    • Bensoussan, A.1    Lions, J.L.2
  • 5
    • 85084706572 scopus 로고    scopus 로고
    • Optimal stopping in mean field games, an obstacle problem approach
    • Bertucci, Charles, Optimal stopping in mean field games, an obstacle problem approach. J. Math. Pures Appl., 2017.
    • (2017) J. Math. Pures Appl.
    • Bertucci, C.1
  • 6
    • 85047222067 scopus 로고    scopus 로고
    • Proximal methods for stationary mean field games with local couplings
    • Briceno-Arias, L.M., Kalise, D., Silva, F.J., Proximal methods for stationary mean field games with local couplings. SIAM J. Control Optim. 56:2 (2018), 801–836.
    • (2018) SIAM J. Control Optim. , vol.56 , Issue.2 , pp. 801-836
    • Briceno-Arias, L.M.1    Kalise, D.2    Silva, F.J.3
  • 7
    • 84969246784 scopus 로고    scopus 로고
    • Parabolic equations in time-dependent domains
    • Calvo, Juan, Novaga, Matteo, Orlandi, Giandomenico, Parabolic equations in time-dependent domains. J. Evol. Equ. 17:2 (2017), 781–804.
    • (2017) J. Evol. Equ. , vol.17 , Issue.2 , pp. 781-804
    • Calvo, J.1    Novaga, M.2    Orlandi, G.3
  • 8
    • 85068762191 scopus 로고    scopus 로고
    • Notes on mean field games
    • Technical report
    • Cardaliaguet, Pierre, Notes on mean field games. Technical report, 2010.
    • (2010)
    • Cardaliaguet, P.1
  • 9
    • 85011536691 scopus 로고    scopus 로고
    • Learning in mean field games: the fictitious play
    • Cardaliaguet, Pierre, Hadikhanloo, Saeed, Learning in mean field games: the fictitious play. ESAIM Control Optim. Calc. Var. 23:2 (2017), 569–591.
    • (2017) ESAIM Control Optim. Calc. Var. , vol.23 , Issue.2 , pp. 569-591
    • Cardaliaguet, P.1    Hadikhanloo, S.2
  • 10
    • 85057948205 scopus 로고    scopus 로고
    • Long time behavior of the master equation in mean-field game theory
    • arXiv preprint
    • Cardaliaguet, Pierre, Porretta, Alessio, Long time behavior of the master equation in mean-field game theory. arXiv preprint arXiv:1709.04215, 2017.
    • (2017)
    • Cardaliaguet, P.1    Porretta, A.2
  • 11
    • 85072069003 scopus 로고    scopus 로고
    • The master equation and the convergence problem in mean field games
    • arXiv preprint
    • Cardaliaguet, Pierre, Delarue, François, Lasry, Jean-Michel, Lions, Pierre-Louis, The master equation and the convergence problem in mean field games. arXiv preprint arXiv:1509.02505, 2015.
    • (2015)
    • Cardaliaguet, P.1    Delarue, F.2    Lasry, J.-M.3    Lions, P.-L.4
  • 12
    • 84942369075 scopus 로고    scopus 로고
    • Second order mean field games with degenerate diffusion and local coupling
    • Cardaliaguet, Pierre, Jameson Graber, P., Porretta, Alessio, Tonon, Daniela, Second order mean field games with degenerate diffusion and local coupling. Nonlinear Differ. Equ. Appl. 22:5 (2015), 1287–1317.
    • (2015) Nonlinear Differ. Equ. Appl. , vol.22 , Issue.5 , pp. 1287-1317
    • Cardaliaguet, P.1    Jameson Graber, P.2    Porretta, A.3    Tonon, D.4
  • 13
    • 84881309217 scopus 로고    scopus 로고
    • Probabilistic analysis of mean-field games
    • Carmona, René, Delarue, François, Probabilistic analysis of mean-field games. SIAM J. Control Optim. 51:4 (2013), 2705–2734.
    • (2013) SIAM J. Control Optim. , vol.51 , Issue.4 , pp. 2705-2734
    • Carmona, R.1    Delarue, F.2
  • 14
    • 85021744328 scopus 로고    scopus 로고
    • Probabilistic Theory of Mean Field Games with Applications I-II
    • Springer
    • Carmona, Rene, Delarue, François, Probabilistic Theory of Mean Field Games with Applications I-II. 2017, Springer.
    • (2017)
    • Carmona, R.1    Delarue, F.2
  • 15
    • 85021710985 scopus 로고    scopus 로고
    • Mean field games of timing and models for bank runs
    • Carmona, Rene, Delarue, François, Lacker, Daniel, Mean field games of timing and models for bank runs. Appl. Math. Optim. 76:1 (2017), 217–260.
    • (2017) Appl. Math. Optim. , vol.76 , Issue.1 , pp. 217-260
    • Carmona, R.1    Delarue, F.2    Lacker, D.3
  • 16
    • 85039934437 scopus 로고    scopus 로고
    • Mean field games with singular controls
    • Fu, Guanxing, Horst, Ulrich, Mean field games with singular controls. SIAM J. Control Optim. 55:6 (2017), 3833–3868.
    • (2017) SIAM J. Control Optim. , vol.55 , Issue.6 , pp. 3833-3868
    • Fu, G.1    Horst, U.2
  • 17
    • 0001046826 scopus 로고    scopus 로고
    • Abstract evolution equations on variable domains: an approach by minimizing movements
    • Gianazza, Ugo, Savaré, Giuseppe, Abstract evolution equations on variable domains: an approach by minimizing movements. Ann. Sc. Norm. Super. Pisa, Cl. Sci. 23:1 (1996), 149–178.
    • (1996) Ann. Sc. Norm. Super. Pisa, Cl. Sci. , vol.23 , Issue.1 , pp. 149-178
    • Gianazza, U.1    Savaré, G.2
  • 18
    • 84931064331 scopus 로고    scopus 로고
    • Obstacle mean-field game problem
    • Gomes, Diogo, Patrizi, Stefania, Obstacle mean-field game problem. Interfaces Free Bound. 17:1 (2015), 55–68.
    • (2015) Interfaces Free Bound. , vol.17 , Issue.1 , pp. 55-68
    • Gomes, D.1    Patrizi, S.2
  • 19
    • 84978437345 scopus 로고    scopus 로고
    • Weakly coupled mean-field game systems
    • Gomes, Diogo A., Patrizi, Stefania, Weakly coupled mean-field game systems. Nonlinear Anal. 144 (2016), 110–138.
    • (2016) Nonlinear Anal. , vol.144 , pp. 110-138
    • Gomes, D.A.1    Patrizi, S.2
  • 20
    • 68849084877 scopus 로고    scopus 로고
    • A reference case for mean field games models
    • Guéant, Olivier, A reference case for mean field games models. J. Math. Pures Appl. 92:3 (2009), 276–294.
    • (2009) J. Math. Pures Appl. , vol.92 , Issue.3 , pp. 276-294
    • Guéant, O.1
  • 22
    • 85039944179 scopus 로고    scopus 로고
    • Mean field games with singular controls of bounded velocity
    • arXiv preprint
    • Guo, Xin, Lee, Joon Seok, Mean field games with singular controls of bounded velocity. arXiv preprint arXiv:1703.04437, 2017.
    • (2017)
    • Guo, X.1    Lee, J.S.2
  • 23
    • 39549087376 scopus 로고    scopus 로고
    • Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle
    • Huang, Minyi, Malhamé, Roland P., Caines, Peter E., et al. Large population stochastic dynamic games: closed-loop McKean-Vlasov systems and the Nash certainty equivalence principle. Commun. Inf. Syst. 6:3 (2006), 221–252.
    • (2006) Commun. Inf. Syst. , vol.6 , Issue.3 , pp. 221-252
    • Huang, M.1    Malhamé, R.P.2    Caines, P.E.3
  • 24
    • 84950272002 scopus 로고
    • A generalization of Brouwer's fixed point theorem
    • Kakutani, Shizuo, A generalization of Brouwer's fixed point theorem. Duke Math. J. 8:3 (1941), 457–459.
    • (1941) Duke Math. J. , vol.8 , Issue.3 , pp. 457-459
    • Kakutani, S.1
  • 25
    • 0000315972 scopus 로고
    • Linear operators leaving invariant a cone in a Banach space
    • Krein, Mark Grigor'evich, Rutman, Moisei Aronovich, Linear operators leaving invariant a cone in a Banach space. Usp. Mat. Nauk 3:1 (1948), 3–95.
    • (1948) Usp. Mat. Nauk , vol.3 , Issue.1 , pp. 3-95
    • Krein, M.G.1    Rutman, M.A.2
  • 26
    • 84933553528 scopus 로고    scopus 로고
    • Mean field games via controlled martingale problems: existence of Markovian equilibria
    • Lacker, Daniel, Mean field games via controlled martingale problems: existence of Markovian equilibria. Stoch. Process. Appl. 125:7 (2015), 2856–2894.
    • (2015) Stoch. Process. Appl. , vol.125 , Issue.7 , pp. 2856-2894
    • Lacker, D.1
  • 27
    • 22844433961 scopus 로고
    • A uniqueness theorem for elliptic quasi-variational inequalities
    • Laetsch, Theodore, A uniqueness theorem for elliptic quasi-variational inequalities. J. Funct. Anal. 18:3 (1975), 286–287.
    • (1975) J. Funct. Anal. , vol.18 , Issue.3 , pp. 286-287
    • Laetsch, T.1
  • 28
    • 33750627999 scopus 로고    scopus 로고
    • Jeux à champ moyen. I–le cas stationnaire
    • Lasry, Jean-Michel, Lions, Pierre-Louis, Jeux à champ moyen. I–le cas stationnaire. C. R. Math. 343:9 (2006), 619–625.
    • (2006) C. R. Math. , vol.343 , Issue.9 , pp. 619-625
    • Lasry, J.-M.1    Lions, P.-L.2
  • 29
    • 33751077273 scopus 로고    scopus 로고
    • Jeux à champ moyen. II–horizon fini et contrôle optimal
    • Lasry, Jean-Michel, Lions, Pierre-Louis, Jeux à champ moyen. II–horizon fini et contrôle optimal. C. R. Math. 343:10 (2006), 679–684.
    • (2006) C. R. Math. , vol.343 , Issue.10 , pp. 679-684
    • Lasry, J.-M.1    Lions, P.-L.2
  • 30
    • 34047127341 scopus 로고    scopus 로고
    • Mean field games
    • Lasry, Jean-Michel, Lions, Pierre-Louis, Mean field games. Jpn. J. Math. 2:1 (2007), 229–260.
    • (2007) Jpn. J. Math. , vol.2 , Issue.1 , pp. 229-260
    • Lasry, J.-M.1    Lions, P.-L.2
  • 31
    • 84865537156 scopus 로고    scopus 로고
    • Cours au college de france
    • 2007
    • Lions, Pierre-Louis, Cours au college de france. www.college-de-france.fr, 2011 2007.
    • (2011)
    • Lions, P.-L.1
  • 32
    • 85056035430 scopus 로고    scopus 로고
    • A mean field game of optimal stopping
    • arXiv preprint
    • Nutz, Marcel, A mean field game of optimal stopping. arXiv preprint arXiv:1605.09112, 2016.
    • (2016)
    • Nutz, M.1
  • 33
    • 85062986559 scopus 로고    scopus 로고
    • Analysis and computation of probability density functions for a 1-d impulsively controlled diffusion process
    • Yaegashi, Yuta, Yoshioka, Hidekazu, Tsugihashi, Kentaro, Fujihara, Masayuki, Analysis and computation of probability density functions for a 1-d impulsively controlled diffusion process. C. R. Math. 357:3 (2019), 306–315.
    • (2019) C. R. Math. , vol.357 , Issue.3 , pp. 306-315
    • Yaegashi, Y.1    Yoshioka, H.2    Tsugihashi, K.3    Fujihara, M.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.