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Volumn 45, Issue 2, 2017, Pages 824-878

Mean-field stochastic differential equations and associated PDES

Author keywords

McKean Vlasov equation; Mean field stochastic differential equation; PDE of mean field type; Value function

Indexed keywords


EID: 85017161972     PISSN: 00911798     EISSN: None     Source Type: Journal    
DOI: 10.1214/15-AOP1076     Document Type: Article
Times cited : (302)

References (21)
  • 1
    • 0040687609 scopus 로고    scopus 로고
    • Nonlinear selfstabilizing processes. I. Existence, invariant probability, propagation of chaos
    • MR1632193
    • BENACHOUR, S., ROYNETTE, B., TALAY, D. and VALLOIS, P. (1998). Nonlinear selfstabilizing processes. I. Existence, invariant probability, propagation of chaos. Stochastic Process. Appl. 75 173-201. MR1632193
    • (1998) Stochastic Process. Appl , vol.75 , pp. 173-201
    • Benachour, S.1    Roynette, B.2    Talay, D.3    Vallois, P.4
  • 3
    • 0031539944 scopus 로고    scopus 로고
    • A stochastic particle method for the McKean-Vlasov and the Burgers equation
    • MR1370849
    • BOSSY, M. and TALAY, D. (1997). A stochastic particle method for the McKean-Vlasov and the Burgers equation. Math. Comp. 66 157-192. MR1370849
    • (1997) Math. Comp , vol.66 , pp. 157-192
    • Bossy, M.1    Talay, D.2
  • 4
    • 69249229620 scopus 로고    scopus 로고
    • Mean-field backward stochastic differential equations: A limit approach
    • MR2546754
    • BUCKDAHN, R., DJEHICHE, B., LI, J. and PENG, S. (2009). Mean-field backward stochastic differential equations: A limit approach. Ann. Probab. 37 1524-1565. MR2546754
    • (2009) Ann. Probab , vol.37 , pp. 1524-1565
    • Buckdahn, R.1    Djehiche, B.2    Li, J.3    Peng, S.4
  • 5
    • 69749102885 scopus 로고    scopus 로고
    • Mean-field backward stochastic differential equations and related partial differential equations
    • MR2568268
    • BUCKDAHN, R., LI, J. and PENG, S. (2009).Mean-field backward stochastic differential equations and related partial differential equations. Stochastic Process. Appl. 119 3133-3154. MR2568268
    • (2009) Stochastic Process. Appl , vol.119 , pp. 3133-3154
    • Buckdahn, R.1    Li, J.2    Peng, S.3
  • 6
    • 85068762191 scopus 로고    scopus 로고
    • (from P. L. Lions' lectures at Collège de France)
    • CARDALIAGUET, P. (2013). Notes on mean field games (from P. L. Lions' lectures at Collège de France). Available at https://www.ceremade.dauphine.fr/~cardalia/.
    • (2013) Notes on mean field games
    • Cardaliaguet, P.1
  • 9
    • 84947717362 scopus 로고    scopus 로고
    • Forward-backward stochastic differential equations and controlled McKean-Vlasov dynamics
    • MR3395471
    • CARMONA, R. and DELARUE, F. (2015). Forward-backward stochastic differential equations and controlled McKean-Vlasov dynamics. Ann. Probab. 43 2647-2700. MR3395471
    • (2015) Ann. Probab , vol.43 , pp. 2647-2700
    • Carmona, R.1    Delarue, F.2
  • 10
    • 0040257213 scopus 로고
    • Dynamics of the McKean-Vlasov equation
    • MR1258884
    • CHAN, T. (1994). Dynamics of the McKean-Vlasov equation. Ann. Probab. 22 431-441. MR1258884
    • (1994) Ann. Probab , vol.22 , pp. 431-441
    • Chan, T.1
  • 11
    • 0030210666 scopus 로고    scopus 로고
    • McKean-Vlasov limit for interacting random processes in random media
    • MR1400186
    • DAI PRA, P. and DEN HOLLANDER, F. (1996). McKean-Vlasov limit for interacting random processes in random media. J. Stat. Phys. 84 735-772. MR1400186
    • (1996) J. Stat. Phys , vol.84 , pp. 735-772
    • Dai Pra, P.1    Den Hollander, F.2
  • 12
    • 0001356070 scopus 로고
    • Large deviations from the McKean-Vlasov limit for weakly interacting diffusions
    • MR0885876
    • DAWSON, D. A. and GäRTNER, J. (1987). Large deviations from the McKean-Vlasov limit for weakly interacting diffusions. Stochastics 20 247-308. MR0885876
    • (1987) Stochastics , vol.20 , pp. 247-308
    • Dawson, D.A.1    Gärtner, J.2
  • 15
    • 21844514446 scopus 로고
    • A class of quasilinear stochastic partial differential equations of McKean-Vlasov type with mass conservation
    • MR1337250
    • KOTELENEZ, P. (1995). A class of quasilinear stochastic partial differential equations of McKean-Vlasov type with mass conservation. Probab. Theory Related Fields 102 159-188 MR1337250
    • (1995) Probab. Theory Related Fields , vol.102 , pp. 159-188
    • Kotelenez, P.1
  • 16
    • 34047127341 scopus 로고    scopus 로고
    • Mean field games
    • MR2295621
    • LASRY, J.-M. and LIONS, P.-L. (2007). Mean field games. Jpn. J. Math. 2 229-260. MR2295621
    • (2007) Jpn. J. Math , vol.2 , pp. 229-260
    • Lasry, J.-M.1    Lions, P.-L.2
  • 20
    • 0001293553 scopus 로고
    • Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated
    • MR0743844
    • SZNITMAN, A.-S. (1984). Nonlinear reflecting diffusion process, and the propagation of chaos and fluctuations associated. J. Funct. Anal. 56 311-336. MR0743844
    • (1984) J. Funct. Anal , vol.56 , pp. 311-336
    • Sznitman, A.-S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.