Product formula and independence criterion for multiple Huang-Cambanis integrals (Q2494881)

Multiple stochastic integrals of \textit{S. T. Huang} and \textit{S. Cambanis} [Ann. Probab. 6, 585--614 (1978; Zbl 0387.60064)] with respect to a general Gaussian process \(X=(X_t, t\in T)\), whose covariance function is of bounded variation on bounded subsets of \(T\times T\), are considered. A product formula for the integrals is derived and a necessary and sufficient condition for independence of multiple Huang-Cambanis integrals is obtained. As an illustration, the results are applied to the special case of multiple integrals with respect to a persistent fractional Brownian motion.