Path and semimartingale properties of chaos processes (Q963036)

This article deals with ``chaos processes'' satisfying some integrability condition, which entails that on the variables of such process, the \(L^p\)-norms are equivalent (at least for some \(p\)'s). This class of stochstic processes contains mainly: -- sums of Wiener-Itô integrals of bounded order; -- integrals with respect to some infinitely divisible random measure (including stable processes); -- limits in probability of polynomials (actually ``tetrahedral'' ones) of bounded degree, evaluated on i.i.d. random variables whose common law is regularly varying. Properties already known for Gaussian processes are extended to this more general framework. In particular path properties, such as absolute continuity of the process has bounded variation, and a series of characterizations of this, in the curve of stationary increments. Decomposition of semimartingales and moving averages of type \(\int^t_0 \varphi(r-s) dM_s\) are also considered.