Weak Characterizations of Stochastic Integrability and Dudley's Theorem in Infinite Dimensions

0392394 - ÚTIA 2015 RIV DE eng J - Journal Article
Ondreját, Martin - Veraar, M.
Weak Characterizations of Stochastic Integrability and Dudley's Theorem in Infinite Dimensions.
Journal of Theoretical Probability. Roč. 27, č. 4 (2014), s. 1350-1374. ISSN 0894-9840. E-ISSN 1572-9230
R&D Projects: GA ČR GAP201/10/0752
Institutional support: RVO:67985556
Keywords : stochastic integration in Banach spaces * almost sure limit theorems * Dudley representation theorem * universal representation theorem * weak characterization of stochastic integrability * Doob representation theorem
Subject RIV: BA - General Mathematics
Impact factor: 0.857, year: 2014
http://library.utia.cas.cz/separaty/2013/SI/ondrejat-0392394.pdf

Weak characterizations of stochastic integrability in Banach spaces are presented as well as their limitations. Results in representation theory for random variables in terms of stochastic integrals are exposed, in particular an infinite dimensional version of Dudley’s representation theorem for random variables and an extension of Doob’s representation for martingales.
Permanent Link: http://hdl.handle.net/11104/0221744