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Smooth solutions of systems of quasilinear parabolic equations

Alain BensoussanJens Frehse — 2002

ESAIM: Control, Optimisation and Calculus of Variations

We consider in this article diagonal parabolic systems arising in the context of stochastic differential games. We address the issue of finding smooth solutions of the system. Such a regularity result is extremely important to derive an optimal feedback proving the existence of a Nash point of a certain class of stochastic differential games. Unlike in the case of scalar equation, smoothness of solutions is not achieved in general. A special structure of the nonlinear hamiltonian seems to be the...

Systems of Bellman Equations to Stochastic Differential Games with Discount Control

Alain BensoussanJens Frehse — 2008

Bollettino dell'Unione Matematica Italiana

We consider two dimensional diagonal elliptic systems Δ u + a u = H ( x , u , u ) which arise from stochastic differential games with discount control. The Hamiltonians H have quadratic growth in 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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