|
|||||
|
|
Some properties of invariant measures of non symmetric dissipative stochastic systems |
|
| Authors: | Giuseppe Da Prato Arnaud Debussche Beniamin Goldys |
| Institution: | (1) Scuola Normale Superiore di Pisa, Piazza dei Cavalieri 7, 56126 Pisa, Italy e-mail: daprato@sns.it, IT;(2) Ecole Normale Supérieure de Cachan, antenne de Bretagne, Campus de Ker Lann, 35170 Bruz, France, FR;(3) School of Mathematics, The University of New South Wales Sydney 2052, Australia, AU |
| Abstract: | We consider transition semigroups generated by stochastic partial differential equations with dissipative nonlinear terms. We prove an integration by part formula and a Logarithmic Sobolev inequality for the invariant measure. No symmetry or reversibility assumptions are made. Furthemore we prove some compactness results on the transition semigroup and on the embedding of the Sobolev spaces based on the invariant measure. We use these results to derive asymptotic properties for a stochastic reaction–diffusion equation. Received: 29 September 2000 / Revised version: 30 May 2001 / Published online: 14 June 2002 |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ | |