Some remarks on tangent martingale difference sequences in $L^1$-spaces
| dc.creator | Cox, Sonja | |
| dc.creator | Veraar, Mark | |
| dc.date | 2008-01-04 | |
| dc.date.accessioned | 2026-07-07T08:52:38Z | |
| dc.date.available | 2026-07-07T08:52:38Z | |
| dc.description | Let X be a Banach space. Suppose that for all $p\in (1, \infty)$ a constant $C_{p,X}$ depending only on X and p exists such that for any two X-valued martingales f and g with tangent martingale difference sequences one has \[\E\|f\|^p \leq C_{p,X} \E\|g\|^p (*).\] This property is equivalent to the UMD condition. In fact, it is still equivalent to the UMD condition if in addition one demands that either f or g satisfy the so-called (CI) condition. However, for some applications it suffices to assume that (*) holds whenever g satisfies the (CI) condition. We show that the class of Banach spaces for which (*) holds whenever only g satisfies the (CI) condition is more general than the class of UMD spaces, in particular it includes the space L^1. We state several problems related to (*) and other decoupling inequalities. | |
| dc.identifier | https://arxiv.org/abs/0801.0695 | |
| dc.identifier | http://arxiv.org/abs/0801.0695 | |
| dc.identifier | Electron. Commun. Probab. 12, 421-433, (2007) | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/145343 | |
| dc.subject | Probability | |
| dc.subject | Functional Analysis | |
| dc.subject | 60B05; 46B09; 60G42 | |
| dc.title | Some remarks on tangent martingale difference sequences in $L^1$-spaces | |
| dc.type | text |