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

我们考虑在Banach空间X中采用值的随机变量的解耦不等式。我们限制了在解耦时显示为条件分布的分布的类别，并表明每个适应的过程都可以通过Haar型展开来近似，其中仅出现预先指定的条件分布。此外，我们表明，在我们的框架中，基础过滤的逐步扩大不会影响解耦特性（特别是，它不会影响所涉及的常数）。作为一个特例，我们处理了解耦二进角（（即，Paley–Walsh）mar的单侧矩不等式，并证明了X的随机积分的Burkholder–Davis–Gundy型不等式可以从解耦X值二进de的不等式中获得T值的过程。