On Decoupling in Banach Spaces
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
Published in
Journal of Theoretical ProbabilityDate
2021Copyright
© The Author(s) 2021
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.
Publisher
SpringerISSN Search the Publication Forum
0894-9840Keywords
Publication in research information system
https://converis.jyu.fi/converis/portal/detail/Publication/52069690
Metadata
Show full item recordCollections
Related funder(s)
Research Council of FinlandFunding program(s)
Academy Project, AoFAdditional information about funding
The first author is supported by the research program VENI Vernieuwingsimpuls with Project Number 639.031.549, which is financed by the Netherlands Organization for Scientific Research (NWO). The second author is supported by the project Stochastic Analysis and Nonlinear Partial Differential Equations, Interactions and Applications of the Academy of Finland with Project Number 298641. The authors wish to thank Mark Veraar, Peter Spreij, and an anonymous referee. The first author would also like to thank Lotte Meijer. Open access funding provided by University of Jyväskylä (JYU). ...License
Related items
Showing items with similar title or keywords.
-
Conditional convex orders and measurable martingale couplings
Leskelä, Lasse; Vihola, Matti (International Statistical Institute; Bernoulli Society for Mathematical Statistics and Probability, 2017)Strassen’s classical martingale coupling theorem states that two random vectors are ordered in the convex (resp. increasing convex) stochastic order if and only if they admit a martingale (resp. submartingale) coupling. By ... -
Decoupling on the Wiener Space, Related Besov Spaces, and Applications to BSDEs
Geiss, Stefan; Ylinen, Juha (American Mathematical Society, 2021)We introduce a decoupling method on the Wiener space to define a wide class of anisotropic Besov spaces. The decoupling method is based on a general distributional approach and not restricted to the Wiener space. The class ... -
Uniform measure density condition and game regularity for tug-of-war games
Heino, Joonas (International Statistical Institute; Bernoulli Society for Mathematical Statistics and Probability, 2018)We show that a uniform measure density condition implies game regularity for all 2 < p < ∞ in a stochastic game called “tug-of-war with noise”. The proof utilizes suitable choices of strategies combined with estimates for ... -
Decoupling on the Wiener space and variational estimates for BSDEs
Ylinen, Juha (University of Jyväskylä, 2015) -
Chaotic decompositions of the Lévy-Itô space
Luuri, Eetu (2024)Tämän tutkielman aiheena ovat erilaiset kaoottiset hajotelmat Lévy prosessien funktionaaleille. Näillä hajotelmilla pyritään esittämään kyseiset funktionaalit iteroitujen integraalien summana tietyn, keskenään ortogonaalisten ...