Multiple Stable Stochastic Integrals: Series Representation and Absolute Continuity of Their Law

Abstract

We study multiple stable stochastic integrals. We begin with a definition of these integrals using a generalization of the LePage representation as Samorodnitsky et al. in Ref. 15 but with a simplified probabilistic background and for general stable measure when 0<α<1 and for symmetric stable measure when 1≤α<2. This representation allows to study the law of multiple stable integrals. We prove they are absolutely continuous using a stratification method on the Skorokhod space on which we have previously taken back the problem.