On decoupling, series expansions, and tail behavior of chaos processes (Q1209210)

The authors start their motivation with a special type of the so-called chaos processes: the isonormal chaos processes associated to a probability measure. If \((\Omega,\Sigma,\text{Pr})\) is a probability space and \(H\) is a closed subspace of \(L_ 2(\Omega,\Sigma,\text{Pr})\) all of whose elements are normal random variables, it is defined the \(H\)- chaos probability (Borel) measure of order \(m\). Then it is introduced the definition of the weak \(B\)-valued and \(H\)-chaos random variables of order \(m\), where \(B\) is an originally given Banach space. The paper presents some important advances on the chaos random variables in connection with decoupling, an almost sure representation and integrability.