Bellman equation: Difference between revisions
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imported>Luis (Created page with "The Bellman equation is the equality \[ \sup_{a \in \mathcal{A}} \, L_a u(x) = f(x), \] where $L_a$ is some family of linear integro-differential operators indexed by an arbitrar...") |
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Revision as of 14:38, 27 May 2011
The Bellman equation is the equality \[ \sup_{a \in \mathcal{A}} \, L_a u(x) = f(x), \] where $L_a$ is some family of linear integro-differential operators indexed by an arbitrary set $\mathcal{A}$.
The equation appears naturally in problems of stochastic control with Levy processes.
The equation is uniformly elliptic with respect to any class $\mathcal{L}$ that contains all the operators $L_a$.