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The purpose of this paper is to provide a detailed probabilistic analysis of the optimal control of nonlinear stochastic dynamical systems of the McKean Vlasov type.
A class of markov processes associated with nonlinear parabolic equations
H.P. McKean · 1966
Earlier work this paper cites.
Propagation of chaos for a class of nonlinear parabolic equations
H.P. McKean · 1967
Earlier work this paper cites.
Topics in propagation of chaos
A.S. Sznitman · 1989
Earlier work this paper cites.
Adapted solution of a backward stochastic differential equation
E. Pardoux and S. Peng · 1990
Earlier work this paper cites.
Mass Transportation Problems I: Theory
S.T. Rachev and L. Ruschendorf · 1998
Earlier work this paper cites.
Fully coupled forward-backward stochastic differential equations and applications to optimal control
S. Peng and Z. Wu · 1999
Earlier work this paper cites.
On the existence and uniqueness of solutions to FBSDEs in a non-degenerate case
F. Delarue · 2002
Cited alongside, same era.
Gradient flows in metric spaces and in the Wasserstein space of probability measures
L. Ambrosio, N. Gigli, and G. Savaré · 2004
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Nonlinear SDEs driven by Lévy processes and related PDEs
B. Jourdain, S. Meleard, and W. Woyczynski · 2008
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Mean-field backward stochastic differential equations: A limit approach
R. Buckdahn, B. Djehiche, J. Li, and S. Peng · 2009
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Optimal Transport, Old and New
C. Villani · 2009
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A maximum principle for sdes of mean-field type
D. Andersson and B. Djehiche · 2010
Cited alongside, same era.
Notes on mean field games
P. Cardaliaguet · 2010
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Z. Wu and Z. Yu · 2010
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Linear quadratic mean field games
A. Bensoussan, K.C.J. Sung, S.C.P. Yam, and S.P. Yung · 2011
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Probabilistic analysis of mean field games
R. Carmona and F. Delarue · 2012
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Control of McKean-Vlasov versus Mean Field Games
R. Carmona, F. Delarue, and A. Lachapelle · 2012
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Mean field forward-backward stochastic differential equations
R. Carmona and F. Delarue
Cited in the paper.