| Full text | |
| Author(s): |
Abreu, Jamil
;
Haak, Bernhard
;
van Neerven, Jan
Total Authors: 3
|
| Document type: | Journal article |
| Source: | JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES; v. 88, p. 21-pg., 2013-08-01. |
| 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) |