Systems of Bellman Equations to Stochastic Differential Games with Discount Control
Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 3, pp. 663-681
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We consider two dimensional diagonal elliptic systems $\Delta u + au = H(x, u, \nabla u)$ which arise from stochastic differential games with discount control. The Hamiltonians $H$ have quadratic growth in $\nabla u$ and a special structure which has notyet been covered by regularity theory. Without smallness condition on $H$, the existence of a regular solution is established.
@article{BUMI_2008_9_1_3_a8,
author = {Bensoussan, Alain and Frehse, Jens},
title = {Systems of {Bellman} {Equations} to {Stochastic} {Differential} {Games} with {Discount} {Control}},
journal = {Bollettino della Unione matematica italiana},
pages = {663--681},
publisher = {mathdoc},
volume = {Ser. 9, 1},
number = {3},
year = {2008},
zbl = {1190.49045},
mrnumber = {2455338},
language = {en},
url = {http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_3_a8/}
}
TY - JOUR AU - Bensoussan, Alain AU - Frehse, Jens TI - Systems of Bellman Equations to Stochastic Differential Games with Discount Control JO - Bollettino della Unione matematica italiana PY - 2008 SP - 663 EP - 681 VL - 1 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_3_a8/ LA - en ID - BUMI_2008_9_1_3_a8 ER -
%0 Journal Article %A Bensoussan, Alain %A Frehse, Jens %T Systems of Bellman Equations to Stochastic Differential Games with Discount Control %J Bollettino della Unione matematica italiana %D 2008 %P 663-681 %V 1 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_3_a8/ %G en %F BUMI_2008_9_1_3_a8
Bensoussan, Alain; Frehse, Jens. Systems of Bellman Equations to Stochastic Differential Games with Discount Control. Bollettino della Unione matematica italiana, Série 9, Tome 1 (2008) no. 3, pp. 663-681. http://geodesic.mathdoc.fr/item/BUMI_2008_9_1_3_a8/