The stochastic Weiss conjecture for bounded analytic semigroups
Language
en
Article de revue
This item was published in
Journal London Mathematical Society. 2013-03-13, vol. 88, n° 1, p. 181-201
English Abstract
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 ...Read more >
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].Read less <
ANR Project
Aux frontières de l'analyse Harmonique - ANR-12-BS01-0013
Origin
Hal imported