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In this paper, we deal with a class of mean-field backward stochastic differential equations (BSDEs) related to finite state, continuous time Markov chains. We obtain the existence and uniqueness theorem and a comparison theorem for solutions of one-dimensional mean-field BSDEs under Lipschitz condition.
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참고문헌 (24)
참고문헌 신청
D. Crisan / 2010 / Approximate McKean-Vlasov representations for a class of SPDEs / Stochastics 82 : 53 ~ 68
E. Pardoux / 1990 / Adapted solution of a backward stochastic differential equation / Systems Control Lett 14 (1) : 55 ~ 61
H. McKean / 1966 / A class of Markov processes associated with nonlinear parabolic equations / Proc. Nat. Acad. Sci. U.S.A 56 : 1907 ~ 1911
J. Lasry / 2007 / Mean field games / Jpn J. Math 2 (1) : 229 ~ 260
J. Li / 2014 / Reflected Mean-Field Backward Stochastic Differential Equations, Approximation and Associated Nonlinear PDEs / J. Math. Anal. Appl 413 (1) : 47 ~ 68
E. Pardoux / 1990 / Adapted solution of a backward stochastic differential equation / Systems Control Lett 14 (1) : 55 ~ 61
H. McKean / 1966 / A class of Markov processes associated with nonlinear parabolic equations / Proc. Nat. Acad. Sci. U.S.A 56 : 1907 ~ 1911
J. Lasry / 2007 / Mean field games / Jpn J. Math 2 (1) : 229 ~ 260
J. Li / 2014 / Reflected Mean-Field Backward Stochastic Differential Equations, Approximation and Associated Nonlinear PDEs / J. Math. Anal. Appl 413 (1) : 47 ~ 68
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