The stochastic Weiss conjecture for bounded analytic semigroups
hal.structure.identifier | Instituto de Matem atica | |
dc.contributor.author | ABREU, Jamil | |
hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
dc.contributor.author | HAAK, Bernhard Hermann | |
hal.structure.identifier | Analysis group | |
dc.contributor.author | VAN NEERVEN, Jan | |
dc.date.accessioned | 2024-04-04T02:23:20Z | |
dc.date.available | 2024-04-04T02:23:20Z | |
dc.date.issued | 2013-03-13 | |
dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189730 | |
dc.description.abstractEn | Suppose that A admits a bounded H^infty-calculus of angle less than pi/2 on a Banach space E which has Pisier's property (alpha ), let B be a bounded linear operator from a Hilbert space H into the extrapolation space E_{-1} of E with respect to A, and let W_H denote an H-cylindrical Brownian motion. Let gamma(H;E) denote the space of all gamma-radonifying operators from H to E. We prove that the following assertions are equivalent: (a) the stochastic Cauchy problem dU(t) = AU(t) dt + B dWH(t) admits an invariant measure on E; (b) (-A)^{-1/2} B \in gamma(H;E); (c) the Gaussian sum \sum \ga_n 2^{n/2} R(2^n;A)B converges in gamma(H;E) in probability. This solves the stochastic Weiss conjecture of [8]. | |
dc.description.sponsorship | Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013 | |
dc.language.iso | en | |
dc.rights.uri | http://hal.archives-ouvertes.fr/licences/copyright/ | |
dc.title.en | The stochastic Weiss conjecture for bounded analytic semigroups | |
dc.type | Article de revue | |
dc.identifier.doi | 10.1112/jlms/jdt003 | |
dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
bordeaux.journal | Journal London Mathematical Society | |
bordeaux.page | 181-201 | |
bordeaux.volume | 88 | |
bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
bordeaux.issue | 1 | |
bordeaux.institution | Université de Bordeaux | |
bordeaux.institution | Bordeaux INP | |
bordeaux.institution | CNRS | |
bordeaux.peerReviewed | oui | |
hal.identifier | hal-00771883 | |
hal.version | 1 | |
hal.popular | non | |
hal.audience | Internationale | |
hal.origin.link | https://hal.archives-ouvertes.fr//hal-00771883v1 | |
bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Journal%20London%20Mathematical%20Society&rft.date=2013-03-13&rft.volume=88&rft.issue=1&rft.spage=181-201&rft.epage=181-201&rft.au=ABREU,%20Jamil&HAAK,%20Bernhard%20Hermann&VAN%20NEERVEN,%20Jan&rft.genre=article |
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