TY  - JOUR
ID  - publications18330
UR  - http://tse-fr.eu/pub/29333
IS  - n° 3
A1  - Bensoussan, Alain
A1  - Frehse, Jens
A1  - Grün, Christine
N2  - We consider a general Bellman type system of parabolic partial differential equations with a special coupling in the zero order terms. We show the existence of solutions in Lp((0,T);W2,p(O))nW1,p((0,T)×O) by establishing suitable a priori bounds. The system is related to a certain non zero sum stochastic differential game with a maximum of two players. The players control a diffusion in order to minimise a certain cost functional. During the game it is possible that present players may die or a new player may appear. We assume that the death, respectively the birth time of a player is exponentially distributed with intensities that depend on the diffusion and the controls of the players who are alive.
VL  - vol. 13
TI  - On a system of PDEs associated to a game with a varying number of players
AV  - none
EP  - 639
Y1  - 2015///
PB  - International Press
JF  - Communications in Mathematical Sciences
KW  - Bellman systems
KW  - regularity for PDEs
KW  - Nash points
KW  - stochastic differential games
SN  - 1539-6746
SP  - 623
ER  -