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Ergodic Type Bellman Equations of First Order with Quadratic Hamiltonian

Journal Article · · Applied Mathematics and Optimization
 [1]
  1. Nagoya University, Graduate School of Information Science (Japan)
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 Schroedinger 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 Schroedinger operator by an invariant measure.
OSTI ID:
21241903
Journal Information:
Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 1 Vol. 59; ISSN 0095-4616
Country of Publication:
United States
Language:
English

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