Second order parabolic Hamilton–Jacobi–Bellman equations in Hilbert spaces and stochastic control: approach
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| Title: | Second order parabolic Hamilton–Jacobi–Bellman equations in Hilbert spaces and stochastic control: approach |
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| Authors: | Goldys, B.1 B.Goldys@unsw.edu.au, Gozzi, F.2 gozzi@mail.dm.unipi.it |
| Source: | Stochastic Processes & Their Applications. Dec2006, Vol. 116 Issue 12, p1932-1963. 32p. |
| Subjects: | Hilbert space, Banach spaces, Integer programming, Systems engineering |
| Abstract: | Abstract: We study a Hamilton–Jacobi–Bellman equation related to the optimal control of a stochastic semilinear equation on a Hilbert space . We show the existence and uniqueness of solutions to the HJB equation and prove the existence and uniqueness of feedback controls for the associated control problem via dynamic programming. The main novelty is that we look for solutions in the space , where is an invariant measure for an associated uncontrolled process. This allows us to treat controlled systems with degenerate diffusion term that are not covered by the existing literature. In particular, we prove the existence and uniqueness of solutions and obtain the optimal feedbacks for controlled stochastic delay equations and for the first order stochastic PDE’s arising in economic and financial models. [Copyright &y& Elsevier] |
| Copyright of Stochastic Processes & Their Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 23051983 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Second order parabolic Hamilton–Jacobi–Bellman equations in Hilbert spaces and stochastic control: approach – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Goldys%2C+B%2E%22">Goldys, B.</searchLink><relatesTo>1</relatesTo><i> B.Goldys@unsw.edu.au</i><br /><searchLink fieldCode="AR" term="%22Gozzi%2C+F%2E%22">Gozzi, F.</searchLink><relatesTo>2</relatesTo><i> gozzi@mail.dm.unipi.it</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Stochastic+Processes+%26+Their+Applications%22">Stochastic Processes & Their Applications</searchLink>. Dec2006, Vol. 116 Issue 12, p1932-1963. 32p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Hilbert+space%22">Hilbert space</searchLink><br /><searchLink fieldCode="DE" term="%22Banach+spaces%22">Banach spaces</searchLink><br /><searchLink fieldCode="DE" term="%22Integer+programming%22">Integer programming</searchLink><br /><searchLink fieldCode="DE" term="%22Systems+engineering%22">Systems engineering</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Abstract: We study a Hamilton–Jacobi–Bellman equation related to the optimal control of a stochastic semilinear equation on a Hilbert space . We show the existence and uniqueness of solutions to the HJB equation and prove the existence and uniqueness of feedback controls for the associated control problem via dynamic programming. The main novelty is that we look for solutions in the space , where is an invariant measure for an associated uncontrolled process. This allows us to treat controlled systems with degenerate diffusion term that are not covered by the existing literature. In particular, we prove the existence and uniqueness of solutions and obtain the optimal feedbacks for controlled stochastic delay equations and for the first order stochastic PDE’s arising in economic and financial models. [Copyright &y& Elsevier] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Stochastic Processes & Their Applications is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.spa.2006.05.006 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 32 StartPage: 1932 Subjects: – SubjectFull: Hilbert space Type: general – SubjectFull: Banach spaces Type: general – SubjectFull: Integer programming Type: general – SubjectFull: Systems engineering Type: general Titles: – TitleFull: Second order parabolic Hamilton–Jacobi–Bellman equations in Hilbert spaces and stochastic control: approach Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Goldys, B. – PersonEntity: Name: NameFull: Gozzi, F. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2006 Type: published Y: 2006 Identifiers: – Type: issn-print Value: 03044149 Numbering: – Type: volume Value: 116 – Type: issue Value: 12 Titles: – TitleFull: Stochastic Processes & Their Applications Type: main |
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