Bensoussan, Alain and Frehse, Jens:
Systems of Bellman Equations to Stochastic Differential Games with Discount Control
Bollettino dell'Unione Matematica Italiana Serie 9 1 (2008), fasc. n.3, p. 663-681, (English)
pdf (499 Kb), djvu (176 Kb). | MR 2455338 | Zbl 1190.49045
Sunto
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.
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Con il contributo del Ministero per i Beni e le Attività Culturali