TY - JOUR
T1 - Bellman Systems with Mean Field Dependent Dynamics
AU - BENSOUSSAN, Alain
AU - BULÍČEK, Miroslav
AU - FREHSE, Jens
PY - 2018/5
Y1 - 2018/5
N2 - The authors deal with nonlinear elliptic and parabolic systems that are the
Bellman like systems associated to stochastic differential games with mean field dependent
dynamics. The key novelty of the paper is that they allow heavily mean field dependent
dynamics. This in particular leads to a system of PDE’s with critical growth, for which
it is rare to have an existence and/or regularity result. In the paper, they introduce a
structural assumptions that cover many cases in stochastic differential games with mean
field dependent dynamics for which they are able to establish the existence of a weak
solution. In addition, the authors present here a completely new method for obtaining the
maximum/minimum principles for systems with critical growths, which is a starting point
for further existence and also qualitative analysis.
AB - The authors deal with nonlinear elliptic and parabolic systems that are the
Bellman like systems associated to stochastic differential games with mean field dependent
dynamics. The key novelty of the paper is that they allow heavily mean field dependent
dynamics. This in particular leads to a system of PDE’s with critical growth, for which
it is rare to have an existence and/or regularity result. In the paper, they introduce a
structural assumptions that cover many cases in stochastic differential games with mean
field dependent dynamics for which they are able to establish the existence of a weak
solution. In addition, the authors present here a completely new method for obtaining the
maximum/minimum principles for systems with critical growths, which is a starting point
for further existence and also qualitative analysis.
KW - Stochastic games
KW - Bellman equation
KW - Mean field equation
KW - Nonlinear elliptic equations
KW - Weak solution
KW - Maximum principle
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UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85048127930&origin=recordpage
U2 - 10.1007/s11401-018-0078-4
DO - 10.1007/s11401-018-0078-4
M3 - 21_Publication in refereed journal
VL - 39
SP - 461
EP - 486
JO - Chinese Annals of Mathematics. Series B
JF - Chinese Annals of Mathematics. Series B
SN - 0252-9599
IS - 3
ER -