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|Type:||Artigo de periódico|
|Title:||The stochastic Weiss conjecture for bounded analytic semigroups|
van Neerven, J
|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 .|
|Editor:||Oxford Univ Press|
|Appears in Collections:||Artigos e Materiais de Revistas Científicas - Unicamp|
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