Sharp moment inequalities for differentially subordinated martingales
Studia Mathematica (2010)
- Volume: 201, Issue: 2, page 103-131
- ISSN: 0039-3223
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topAdam Osękowski. "Sharp moment inequalities for differentially subordinated martingales." Studia Mathematica 201.2 (2010): 103-131. <http://eudml.org/doc/285737>.
@article{AdamOsękowski2010,
abstract = {We determine the optimal constants $C_\{p,q\}$ in the moment inequalities
$||g||_\{p\} ≤ C_\{p,q\} ||f||_\{q\}$, 1 ≤ p< q< ∞,
where f = (fₙ), g = (gₙ) are two martingales, adapted to the same filtration, satisfying
|dgₙ| ≤ |dfₙ|, n = 0,1,2,...,
with probability 1. Furthermore, we establish related sharp estimates
||g||₁ ≤ supₙΦ(|fₙ|) + L(Φ),
where Φ is an increasing convex function satisfying certain growth conditions and L(Φ) depends only on Φ.},
author = {Adam Osękowski},
journal = {Studia Mathematica},
language = {eng},
number = {2},
pages = {103-131},
title = {Sharp moment inequalities for differentially subordinated martingales},
url = {http://eudml.org/doc/285737},
volume = {201},
year = {2010},
}
TY - JOUR
AU - Adam Osękowski
TI - Sharp moment inequalities for differentially subordinated martingales
JO - Studia Mathematica
PY - 2010
VL - 201
IS - 2
SP - 103
EP - 131
AB - We determine the optimal constants $C_{p,q}$ in the moment inequalities
$||g||_{p} ≤ C_{p,q} ||f||_{q}$, 1 ≤ p< q< ∞,
where f = (fₙ), g = (gₙ) are two martingales, adapted to the same filtration, satisfying
|dgₙ| ≤ |dfₙ|, n = 0,1,2,...,
with probability 1. Furthermore, we establish related sharp estimates
||g||₁ ≤ supₙΦ(|fₙ|) + L(Φ),
where Φ is an increasing convex function satisfying certain growth conditions and L(Φ) depends only on Φ.
LA - eng
UR - http://eudml.org/doc/285737
ER -
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