On Decoupling in Banach Spaces

Abstract We consider decoupling inequalities for random variables taking values in a Banach space X . restrict the class of distributions that appear as conditional while and show each adapted process can be approximated by Haar-type expansion which only pre-specified appear. Moreover, we our framework progressive enlargement underlying filtration does not affect properties (in particular, it constants involved). As special case, deal with one-sided moment decoupled dyadic (i.e., Paley–Walsh) martingales Burkholder–Davis–Gundy-type stochastic integrals -valued processes obtained from martingales.