6533b854fe1ef96bd12aec78

RESEARCH PRODUCT

On decoupling in Banach spaces

Sonja CoxStefan Geiss

subject

Statistics and ProbabilityPure mathematicsGeneral MathematicsBanach space01 natural sciences010104 statistics & probabilityFOS: MathematicsFiltration (mathematics)decoupling in Banach spaces0101 mathematicsSpecial casestokastiset prosessitMathematicsMathematics::Functional Analysisdyadic martingalesProbability (math.PR)010102 general mathematicsDecoupling (cosmology)Conditional probability distributionBanachin avaruudetAdapted processMoment (mathematics)regular conditional probabilities60E15 60H05 46B09stochastic integrationStatistics Probability and UncertaintyfunktionaalianalyysiRandom variableMathematics - Probability

description

AbstractWe 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.

yearjournalcountryeditionlanguage
2021-03-14
http://arxiv.org/abs/1805.12377