O tober WSPC Pro eedings Trim Size: 75in x 5in suquet revision

Niveau: Supérieur, Master, Bac+5
O tober 19, 2006 18:17 WSPC - Pro eedings Trim Size: 9.75in x 6.5in suquet-revision 1 REPRODUCING KERNEL HILBERT SPACES AND RANDOM MEASURES ChARLES SUQUET Laboratoire P. Painlevé, UMR CNRS 8524, Bât M2, Cité S ientique, Université Lille I F59655 Villeneuve d'As q Cedex, Fran e We show how to use Guilbart's embedding of signed measures into a R.K.H.S. to study some limit theorems for random measures and sto hasti pro esses. Key words: Mathemati s Subje t Classi ation: 1. R.K.H.S. and metri s on signed measures In the late seventies, C. Guilbart [4, 5? introdu ed an embedding into a reprodu - ing kernel Hilbert spa e (R.K.H.S.) H of the spa e M of signed measures on some topologi al spa e X. He hara terized the inner produ ts on M indu ing the weak topology on the subspa e M+ of bounded positive measures and established in this setting a Glivenko-Cantelli theorem with appli ations to estimation and hypothesis testing. In this ontribution we present a onstru tive approa h of Guilbart's em- bedding following [20?. This embedding provides a Hilbertian framework for signed random measures.

• wspc - pro eedings


• let µ•1


• measure


• positive measure


• random measures


• topologi al dual