Bellman Systems with Mean Field Dependent Dynamics
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
Author(s)
Detail(s)
| Original language | English |
|---|---|
| Pages (from-to) | 461-486 |
| Journal / Publication | Chinese Annals of Mathematics. Series B |
| Volume | 39 |
| Issue number | 3 |
| Online published | 28 Apr 2018 |
| Publication status | Published - May 2018 |
Link(s)
Abstract
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.
Research Area(s)
- Stochastic games, Bellman equation, Mean field equation, Nonlinear elliptic equations, Weak solution, Maximum principle
Citation Format(s)
Bellman Systems with Mean Field Dependent Dynamics. / BENSOUSSAN, Alain; BULÍČEK, Miroslav; FREHSE, Jens.
In: Chinese Annals of Mathematics. Series B, Vol. 39, No. 3, 05.2018, p. 461-486.
In: Chinese Annals of Mathematics. Series B, Vol. 39, No. 3, 05.2018, p. 461-486.
Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review
