Two Inequalities for the First Moments of a Martingale, its Square Function and its Maximal Function

Adam Osękowski. "Two Inequalities for the First Moments of a Martingale, its Square Function and its Maximal Function." Bulletin of the Polish Academy of Sciences. Mathematics 53.4 (2005): 441-449. <http://eudml.org/doc/281004>.

@article{AdamOsękowski2005,
abstract = { Given a Hilbert space valued martingale (Mₙ), let (M*ₙ) and (Sₙ(M)) denote its maximal function and square function, respectively. We prove that 𝔼|Mₙ| ≤ 2𝔼 Sₙ(M), n=0,1,2,..., 𝔼 M*ₙ ≤ 𝔼 |Mₙ| + 2𝔼 Sₙ(M), n=0,1,2,.... The first inequality is sharp, and it is strict in all nontrivial cases. },
author = {Adam Osękowski},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {martingale; square function; maximal function; moment inequality},
language = {eng},
number = {4},
pages = {441-449},
title = {Two Inequalities for the First Moments of a Martingale, its Square Function and its Maximal Function},
url = {http://eudml.org/doc/281004},
volume = {53},
year = {2005},
}

TY - JOUR
AU - Adam Osękowski
TI - Two Inequalities for the First Moments of a Martingale, its Square Function and its Maximal Function
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2005
VL - 53
IS - 4
SP - 441
EP - 449
AB - Given a Hilbert space valued martingale (Mₙ), let (M*ₙ) and (Sₙ(M)) denote its maximal function and square function, respectively. We prove that 𝔼|Mₙ| ≤ 2𝔼 Sₙ(M), n=0,1,2,..., 𝔼 M*ₙ ≤ 𝔼 |Mₙ| + 2𝔼 Sₙ(M), n=0,1,2,.... The first inequality is sharp, and it is strict in all nontrivial cases.
LA - eng
KW - martingale; square function; maximal function; moment inequality
UR - http://eudml.org/doc/281004
ER -