A1 Journal article (refereed)
On Decoupling in Banach Spaces (2021)

Cox, S., & Geiss, S. (2021). On Decoupling in Banach Spaces. Journal of Theoretical Probability, 34(3), 1179-1212. https://doi.org/10.1007/s10959-021-01085-6

JYU authors or editors

Publication details

All authors or editors: Cox, Sonja; Geiss, Stefan

Journal or series: Journal of Theoretical Probability

ISSN: 0894-9840

eISSN: 1572-9230

Publication year: 2021

Publication date: 14/03/2021

Volume: 34

Issue number: 3

Pages range: 1179-1212

Publisher: Springer

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1007/s10959-021-01085-6

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/74725

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1805.12377

Abstract

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.

Keywords: stochastic processes; functional analysis; Banach spaces

Free keywords: decoupling in Banach spaces; regular conditional probabilities; dyadic martingales; stochastic integration

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Ministry reporting: Yes

Reporting Year: 2021

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