Ergodic Type Bellman Equations of First Order with Quadratic Hamiltonian

Ergodic Type Bellman Equations of First Order with Quadratic Hamiltonian We consider Bellman equations of ergodic type in first order. The Hamiltonian is quadratic on the first derivative of the solution. We study the structure of viscosity solutions and show that there exists a critical value among the solutions. It is proved that the critical value has the representation by the long time average of the kernel of the max-plus Schrödinger type semigroup. We also characterize the critical value in terms of an invariant density in max-plus sense, which can be understood as a counterpart of the characterization of the principal eigenvalue of the Schrödinger operator by an invariant measure. Applied Mathematics and Optimization Springer Journals

Ergodic Type Bellman Equations of First Order with Quadratic Hamiltonian

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Copyright © 2009 by Springer Science+Business Media, LLC
Mathematics; Numerical and Computational Methods ; Mathematical Methods in Physics; Mathematical and Computational Physics; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization
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