𝔖 Bobbio Scriptorium
✦   LIBER   ✦

On Smooth Martingales

✍ Scribed by J.G. Ren

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
290 KB
Volume
120
Category
Article
ISSN
0022-1236

No coin nor oath required. For personal study only.

✦ Synopsis

We prove that all (\boldsymbol{W}_{x})-continuous martingales can be represented as stochastic integrals of smooth integrands and establish a Doob's inequality in terms of ((p, r)) capacity for smooth martingales. '1. 1994 Academic Press. Inc.

πŸ“œ SIMILAR VOLUMES

Vector-Valued Extensions of Operators on
Vector-Valued Extensions of Operators on Martingales
✍ Sergio Antonio Tozoni πŸ“‚ Article πŸ“… 1996 πŸ› Elsevier Science 🌐 English βš– 262 KB

We study weighted inequalities for vector valued extensions of the conditioned square function operator and of the maximal operators of matrix type in the case of regular martingales. As applications we obtain weighted inequalities for vectorvalued extensions of the Hardy᎐Littlewood maximal operator

Weighted Inequalities for Vector Operato
Weighted Inequalities for Vector Operators on Martingales
✍ S.A. Tozoni πŸ“‚ Article πŸ“… 1995 πŸ› Elsevier Science 🌐 English βš– 596 KB

Sufficient conditions are given to get weighted inequalities between two maximal operators on Banach valued regular martingales. As an application we obtain generalizations with weights of the inequalities in the definitions of UMD- and MT-Banach spaces and weighted estimates for the vector valued s

On Schnorr and computable randomness, ma
On Schnorr and computable randomness, martingales, and machines
✍ Rod Downey; Evan Griffiths; Geoffrey Laforte πŸ“‚ Article πŸ“… 2004 πŸ› John Wiley and Sons 🌐 English βš– 269 KB

## Abstract We examine the randomness and triviality of reals using notions arising from martingales and prefix‐free machines. (Β© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

On weighted inequalities for martingale
On weighted inequalities for martingale transform operators
✍ Teresa MartΓ­nez πŸ“‚ Article πŸ“… 2003 πŸ› John Wiley and Sons 🌐 English βš– 224 KB

## Abstract For 1 < __p__ < ∞, the almost surely finiteness of $ E \left(v ^{- {p^{\prime} \over p}} \vert {\cal F}\_{1} \right) $ is a necessary and sufficient condition in order to have almost surely convergence of the sequences {__E__(__f__|β„±~__n__~)} with __f__ ∈ __L__^__p__^(__v dP__). This co