<div class="csl-bib-body">
<div class="csl-entry">Grass, D., Kiseleva, T., & Wagener, F. (2015). Small-noise asymptotics of Hamilton-Jacobi-Bellman equations and bifurcations of stochastic optimal control problems. <i>Communications in Nonlinear Science and Numerical Simulation</i>, <i>22</i>(1–3), 38–54. https://doi.org/10.1016/j.cnsns.2014.09.029</div>
</div>
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dc.identifier.issn
1007-5704
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dc.identifier.uri
http://hdl.handle.net/20.500.12708/150503
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dc.description.abstract
We derive small-noise approximations of the value function of stochastic optimal control problems over an unbounded domain and use these to perform a bifurcation analysis of these problems. The corresponding zero-noise problems may feature indifference (shock, Skiba) points, that is, points of non-differentiability of the value function. Small-noise expansions are obtained in regions of regularity by a singular perturbation analysis of the stochastic Hamilton-Jacobi-Bellman equation; the expansions are matched at the boundaries of these regions to obtain an approximation over the whole state space. From this approximation, a functional geometric invariant is computed: in the presence of zero-noise indifference points, this invariant is multimodal. Regime switching thresholds of the optimally controlled dynamics are defined as those critical points where the invariant takes a local minimum. A change in the number of thresholds is a bifurcation of the dynamics. The concepts are applied to analyse the stochastic lake model.
en
dc.language.iso
en
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dc.publisher
Elsevier
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dc.relation.ispartof
Communications in Nonlinear Science and Numerical Simulation
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dc.subject
Applied Mathematics
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dc.subject
Modeling and Simulation
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dc.subject
Numerical Analysis
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dc.subject
Small noise asymptotics
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dc.subject
Stochastic control
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dc.subject
Regime shifts
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dc.subject
Bifurcations
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dc.title
Small-noise asymptotics of Hamilton-Jacobi-Bellman equations and bifurcations of stochastic optimal control problems
en
dc.type
Artikel
de
dc.type
Article
en
dc.description.startpage
38
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dc.description.endpage
54
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dc.type.category
Original Research Article
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tuw.container.volume
22
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tuw.container.issue
1-3
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tuw.journal.peerreviewed
true
-
tuw.peerreviewed
true
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tuw.researchTopic.id
C6
-
tuw.researchTopic.id
C4
-
tuw.researchTopic.name
Modelling and Simulation
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tuw.researchTopic.name
Mathematical and Algorithmic Foundations
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tuw.researchTopic.value
50
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tuw.researchTopic.value
50
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dcterms.isPartOf.title
Communications in Nonlinear Science and Numerical Simulation
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tuw.publication.orgunit
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research
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tuw.publisher.doi
10.1016/j.cnsns.2014.09.029
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dc.identifier.eissn
1878-7274
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dc.description.numberOfPages
17
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wb.sci
true
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wb.sciencebranch
Mathematik
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wb.sciencebranch
Wirtschaftswissenschaften
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wb.sciencebranch.oefos
1010
-
wb.sciencebranch.oefos
5020
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wb.facultyfocus
Wirtschaftsmathematik und Stochastik
de
wb.facultyfocus
Mathematical Methods in Economics and Stochastics
en
wb.facultyfocus.faculty
E100
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item.openairecristype
http://purl.org/coar/resource_type/c_18cf
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item.openairecristype
http://purl.org/coar/resource_type/c_18cf
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item.grantfulltext
none
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item.fulltext
no Fulltext
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item.openairetype
Artikel
-
item.openairetype
Article
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item.cerifentitytype
Publications
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item.cerifentitytype
Publications
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item.languageiso639-1
en
-
crisitem.author.dept
E105-04 - Forschungsbereich Operations Research und Kontrollsysteme
-
crisitem.author.parentorg
E105 - Institut für Stochastik und Wirtschaftsmathematik