Hardy Martingales and the Unconditional Convergence of Martingales
Copyright policy )Hardy Martingales and the Unconditional Convergence of Martingales
The class of Hardy martingales is introduced. These are martingales taking values in a complex Banach space whose increments, conditional on the past, are in the appropriate Hardy space. Such martingales are plurisubharmonic, and so every \(L^ 1\) bounded Hardy martingale which connverges in probability also converges in norm. Hardy martingales are used to characterize analytic Radon-Nikodym, complex uniformly convex and analytic martingale transform properties: in particular, \(L^ 1\) spaces enjoy these properties.
- University of Cambridge United Kingdom
analytic martingale transform properties, Banach spaces of continuous, differentiable or analytic functions, Martingales with discrete parameter, Hardy martingales
analytic martingale transform properties, Banach spaces of continuous, differentiable or analytic functions, Martingales with discrete parameter, Hardy martingales
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).2 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!