decoupling inequalities
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Author(s):  
Sonja Cox ◽  
Stefan Geiss

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.





2018 ◽  
Vol 168 (2) ◽  
pp. 249-259
Author(s):  
SHAOMING GUO ◽  
CHANGKEUN OH

AbstractWe run an iteration argument due to Pramanik and Seeger, to provide a proof of sharp decoupling inequalities for conical surfaces and for k-cones. These are extensions of results of Łaba and Pramanik to sharp exponents.



2017 ◽  
Vol 133 (1) ◽  
pp. 313-334 ◽  
Author(s):  
Jean Bourgain




Author(s):  
Alexander Drewitz ◽  
Balázs Ráth ◽  
Artëm Sapozhnikov


2011 ◽  
Vol 187 (3) ◽  
pp. 645-706 ◽  
Author(s):  
Alain-Sol Sznitman


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