Multiple stable integrals: Representation, absolute continuity of their law (Q2704632)

The author announces various results concerning the representation and absolute continuity of the law of (multidimensional) stable integrals. He first states, under certain conditions, a representation theorem of LePage type, which generalizes a well-known result in dimension 1 [see Theorem 3.10.1 in \textit{G. Samorodnitsky} and \textit{M. S. Taqqu}, ``Stable non-Gaussian random processes'' (1994)]. Then he uses the famous stratification method of \textit{Yu. A. Davydov} and \textit{M. A. Lifshits} [Itogi Nauki Tekh., Ser. Teor. Veroyatn., Mat. Stat., Teor. Kibern. 22, 61-158 (1984; Zbl 0566.60040)] to give some (natural) conditions ensuring the absolute continuity of the laws of these stable integrals. Sketches of proofs are given, but not the extended proofs, which may be found in another paper [Publ. IRMA, Lille 52 (2000)].