The stochastic Weiss conjecture for bounded analytic semigroups
| Autor: | Bernhard H. Haak, Jamil Abreu, Jan van Neerven |
|---|---|
| Přispěvatelé: | Instituto de Matem atica, Instituto de Matemática, Estatística e Computação Científica [Brésil] (IMECC), Universidade Estadual de Campinas (UNICAMP)-Universidade Estadual de Campinas (UNICAMP), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS), Analysis group, TU Delft, Delft University of Technology (TU Delft)-Delft University of Technology (TU Delft), ANR-12-BS01-0013,HAB,Aux frontières de l'analyse Harmonique(2012) |
| Jazyk: | angličtina |
| Rok vydání: | 2012 |
| Předmět: |
0209 industrial biotechnology
General Mathematics Banach space 02 engineering and technology Space (mathematics) [MATH.MATH-FA]Mathematics [math]/Functional Analysis [math.FA] 01 natural sciences Bounded operator Combinatorics symbols.namesake 020901 industrial engineering & automation Primary: 93B28 Secondary: 35R15 46B09 47B10 47D06 FOS: Mathematics 0101 mathematics Mathematics - Optimization and Control Mathematics Conjecture 010102 general mathematics Probability (math.PR) Hilbert space Functional Analysis (math.FA) Mathematics - Functional Analysis Optimization and Control (math.OC) Gauss sum Bounded function symbols Invariant measure Mathematics - Probability |
| Zdroj: | Journal London Mathematical Society Journal London Mathematical Society, 2013, 88 (1), pp.181-201. ⟨10.1112/jlms/jdt003⟩ |
| DOI: | 10.1112/jlms/jdt003⟩ |
| Popis: | Suppose -A admits a bounded H-infinity calculus of angle less than pi/2 on a Banach space E with 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: (i) the stochastic Cauchy problem dU(t) = AU(t)dt + BdW_H(t) admits an invariant measure on E; (ii) (-A)^{-1/2} B belongs to gamma(H,E); (iii) the Gaussian sum \sum_{n\in\mathbb{Z}} \gamma_n 2^{n/2} R(2^n,A)B converges in gamma(H,E) in probability. This solves the stochastic Weiss conjecture proposed recently by the second and third named authors. Comment: 17 pages; submitted for publication |
| Databáze: | OpenAIRE |
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