Isaacs equation: Difference between revisions
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Revision as of 14:38, 27 May 2011
The Isaacs equation is the equality \[ \sup_{a \in \mathcal{A}} \ \inf_{b \in \mathcal{B}} \ L_{ab} u(x) = f(x), \] where $L_{ab}$ is some family of linear integro-differential operators with two indices $a \in \mathcal A$ and $b \in \mathcal B$.
The equation appears naturally in zero sum stochastic games with Levy processes.
The equation is uniformly elliptic with respect to any class $\mathcal{L}$ that contains all the operators $L_{ab}$.