Optimal control of backward stochastic heat equation with Neumann boundary control and noise
| Autor: | Bin Liu, Huaiqiang Yu |
|---|---|
| Rok vydání: | 2012 |
| Předmět: |
Statistics and Probability
Stochastic partial differential equation Stochastic control Stochastic differential equation Modeling and Simulation Mathematical analysis MathematicsofComputing_NUMERICALANALYSIS Free boundary problem Hamilton–Jacobi–Bellman equation Neumann boundary condition Boundary value problem Mixed boundary condition Mathematics |
| Zdroj: | Stochastics. 85:532-558 |
| ISSN: | 1744-2516 1744-2508 |
| DOI: | 10.1080/17442508.2011.654345 |
| Popis: | This paper considers a stochastic control problem in which the dynamic system is a controlled backward stochastic heat equation with Neumann boundary control and boundary noise and the state must coincide with a given random vector at terminal time. Through defining a proper form of the mild solution for the state equation, the existence and uniqueness of the mild solution is given. As a main result, a global maximum principle for our control problem is presented. The main result is also applied to a backward linear-quadratic control problem in which an optimal control is obtained explicitly as a feedback of the solution to a forward–backward stochastic partial differential equation. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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