On the structure of solutions of ergodic type Bellman equation related to risk-sensitive control. (English) Zbl 1092.60030
The authors consider Bellman equations of ergodic type, with positive quadratic nonlinear term on first-order partial derivatives. They obtain multiple solutions, and they classify them by a global behavior of the underlying diffusion processes. They also prove uniqueness and stability of the solution associated with ergodic diffusion process.
Reviewer: George Stoica (Saint John)
MSC:
| 60J60 | Diffusion processes |
| 60G35 | Signal detection and filtering (aspects of stochastic processes) |
| 60H30 | Applications of stochastic analysis (to PDEs, etc.) |
| 93E20 | Optimal stochastic control |
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