ON NONLINEAR ELLIPTIC BELLMAN SYSTEMS FOR A CLASS OF STOCHASTIC DIFFERENTIAL GAMES IN ARBITRARY DIMENSION
2011
Abstract
We consider nonlinear elliptic Bellman systems which arise in the theory of stochastic differential games. The right-hand sides of the equations (which are called Hamiltonians) may have quadratic growth with respect to the gradient of the unknowns.
Under certain assumptions on the Hamiltonians, that are satisfied for many types of stochastic games, we establish the existence of a regular solution. The main novelty of the paper consists of introducing a new (semi-continuity) method for obtaining the continuity of the solution and the corresponding estimates.