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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

The stochastic Weiss conjecture for bounded analytic semigroups

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Author(s):
Abreu, Jamil [1] ; Haak, Bernhard [2] ; van Neerven, Jan [3]
Total Authors: 3
Affiliation:
[1] Univ Estadual Campinas, Inst Matemat Estat & Comp Cient, BR-13083859 Sao Paulo - Brazil
[2] Univ Bordeaux 1, Inst Math Bordeaux, F-33405 Talence - France
[3] Delft Univ Technol, Delft Inst Appl Math, NL-2600 GA Delft - Netherlands
Total Affiliations: 3
Document type: Journal article
Source: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES; v. 88, n. 1, p. 181-201, AUG 2013.
Web of Science Citations: 0
Abstract

Suppose -A admits a bounded H8-calculus of angle less than p/2 on a Banach space E which has Pisier's property (a), 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 WH denote an H-cylindrical Brownian motion. Let.(H, E) denote the space of all.-radonifying operators from H to E. We prove that the following assertions are equivalent: the stochastic Cauchy problem dU(t) = AU(t) dt + B dW(H)(t) admits an invariant measure on E; (-A)(-1/2) B is an element of gamma(H, E); the Gaussian sum Sigma(n is an element of Z) gamma(n) 2(n/2) R(2(n), A)B converges in gamma(H, E) in probability. This solves the stochastic Weiss conjecture of {[}8]. (AU)

FAPESP's process: 07/08220-9 - Stochastic partial differential equations and Lie Groups
Grantee:Jamil Gomes de Abreu Júnior
Support Opportunities: Scholarships in Brazil - Doctorate (Direct)