Publication:
A stochastic representation for mean curvature type geometric flows

dc.contributor.coauthorTouzi, N.
dc.contributor.departmentDepartment of Mathematics
dc.contributor.kuauthorSoner, Halil Mete
dc.contributor.kuprofileFaculty Member
dc.date.accessioned2024-11-09T13:56:19Z
dc.date.issued2003
dc.description.abstractA smooth solution {Gamma(t)}(tis an element of[0,T]) subset of R-d of a parabolic geometric flow is characterized as the reachability set of a stochastic target problem. In this control problem the controller tries to steer the state process into a given deterministic set T with probability one. The reachability set, V(t), for the target problem is the set of all initial data x from which the state process X-X(v)(t) is an element of T for some control process v. This representation is proved by studying the squared distance function to Gamma(t). For the codimension k mean curvature flow, the state process is dX(t) = root2P dW(t), where W(t) is a d-dimensional Brownian motion, and the control P is any projection matrix onto a (d - k)-dimensional plane. Smooth solutions of the inverse mean curvature flow and a discussion of non smooth solutions are also given.
dc.description.fulltextYES
dc.description.indexedbyWoS
dc.description.indexedbyScopus
dc.description.issue1
dc.description.openaccessYES
dc.description.publisherscopeInternational
dc.description.sponsoredbyTubitakEuN/A
dc.description.sponsorshipN/A
dc.description.versionPublisher version
dc.description.volume59
dc.formatpdf
dc.identifier.doi10.1214/aop/1055425773
dc.identifier.embargoNO
dc.identifier.filenameinventorynoIR00464
dc.identifier.issn0091-1798
dc.identifier.linkhttps://doi.org/10.1214/aop/1055425773
dc.identifier.quartileQ1
dc.identifier.scopus2-s2.0-78649704657
dc.identifier.urihttps://hdl.handle.net/20.500.14288/4057
dc.identifier.wos284592200011
dc.keywordsGeometric flows
dc.keywordsCodimension -K Mean curvature flow
dc.keywordsInverse mean curvature flow
dc.keywordsStochastic target problem
dc.keywordsViscosity solutions
dc.keywordsPlane-curves
dc.keywordsEquations
dc.keywordsSet
dc.keywordsConstraints
dc.keywordsMotion
dc.languageEnglish
dc.publisherInstitute of Mathematical Statistics (IMS)
dc.relation.urihttp://cdm21054.contentdm.oclc.org/cdm/ref/collection/IR/id/557
dc.sourceAnnals of Probability
dc.subjectMathematics
dc.subjectStatistics and probability
dc.titleA stochastic representation for mean curvature type geometric flows
dc.typeJournal Article
dspace.entity.typePublication
local.contributor.kuauthorSoner, Halil Mete
local.publication.orgunit1College of Administrative Sciences and Economics
local.publication.orgunit2Department of Mathematics
relation.isOrgUnitOfPublication2159b841-6c2d-4f54-b1d4-b6ba86edfdbe
relation.isOrgUnitOfPublication.latestForDiscovery2159b841-6c2d-4f54-b1d4-b6ba86edfdbe

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