Ergodic Control for Lévy-Driven Linear Stochastic Equations in Hilbert Spaces
| Autor: | K. Kadlec, Bohdan Maslowski |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
0209 industrial biotechnology
Control and Optimization Applied Mathematics Operator (physics) 010102 general mathematics Mathematical analysis MathematicsofComputing_NUMERICALANALYSIS Hilbert space Boundary (topology) 02 engineering and technology Type (model theory) Optimal control 01 natural sciences Lévy process symbols.namesake 020901 industrial engineering & automation Square-integrable function symbols Point (geometry) 0101 mathematics Mathematics |
| Zdroj: | Applied Mathematics & Optimization. 79:547-565 |
| ISSN: | 1432-0606 0095-4616 |
| Popis: | In this paper, controlled linear stochastic evolution equations driven by square integrable Levy processes are studied in the Hilbert space setting. The control operator may be unbounded which makes the results obtained in the abstract setting applicable to parabolic SPDEs with boundary or point control. The first part contains some preliminary technical results, notably a version of Ito formula which is applicable to weak/mild solutions of controlled equations. In the second part, the ergodic control problem is solved: The feedback form of the optimal control and the formula for the optimal cost are found. As examples, various parabolic type controlled SPDEs are studied. |
| Databáze: | OpenAIRE |
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