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hal.structure.identifierLaboratoire Jacques-Louis Lions [LJLL]
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorAndreev, Roman
hal.structure.identifier
dc.contributor.authorKirchner, Kristin
dc.date.accessioned2018-02-16T13:59:33Z
dc.date.available2018-02-16T13:59:33Z
dc.date.issued2016
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17410
dc.language.isoenen
dc.subjectprojective and injective tensor producten
dc.subjectHilbert tensor producten
dc.subjectvariational problemsen
dc.subjectmultiplicative noiseen
dc.subjectadditive noiseen
dc.subjectStochastic ordinary differential equationsen
dc.subjectPetrov-Galerkin discretizationsen
dc.subject.ddc515en
dc.titleNumerical methods for the 2nd moment of stochastic ODEsen
dc.typeDocument de travail / Working paper
dc.description.abstractenNumerical methods for stochastic ordinary differential equations typically estimate moments of the solution from sampled paths. Instead, in this paper we directly target the deterministic equation satisfied by the first and second moments. For the canonical examples with additive noise (Ornstein-Uhlenbeck process) or multiplicative noise (geometric Brownian motion) we derive these deterministic equations in variational form and discuss their well-posedness in detail. Notably, the second moment equation in the multiplicative case is naturally posed on projective-injective tensor products as trial-test spaces. We propose Petrov-Galerkin discretizations based on tensor product piecewise polynomials and analyze their stability and convergence in the natural norms.en
dc.identifier.citationpages26en
dc.relation.ispartofseriestitlecahier de recherche CEREMADE- Paris-Dauphineen
dc.subject.ddclabelAnalyseen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
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