A Weak-Type Inequality for Submartingales and Itô Processes

Adam Osękowski

Bulletin of the Polish Academy of Sciences. Mathematics (2015)

  • Volume: 63, Issue: 1, page 73-88
  • ISSN: 0239-7269

Abstract

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Let α ∈ [0,1] be a fixed parameter. We show that for any nonnegative submartingale X and any semimartingale Y which is α-subordinate to X, we have the sharp estimate ∥ Y ∥ W ≤ ( 2 ( α + 1 ) ² ) / ( 2 α + 1 ) ∥ X ∥ L ∞ . Here W is the weak- L ∞ space introduced by Bennett, DeVore and Sharpley. The inequality is already sharp in the context of α-subordinate Itô processes.

How to cite

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Adam Osękowski. "A Weak-Type Inequality for Submartingales and Itô Processes." Bulletin of the Polish Academy of Sciences. Mathematics 63.1 (2015): 73-88. <http://eudml.org/doc/281306>.

@article{AdamOsękowski2015,
abstract = {Let α ∈ [0,1] be a fixed parameter. We show that for any nonnegative submartingale X and any semimartingale Y which is α-subordinate to X, we have the sharp estimate $∥Y∥_\{W\} ≤ (2(α+1)²)/(2α+1) ∥X∥_\{L^∞\}$. Here W is the weak-$L^∞$ space introduced by Bennett, DeVore and Sharpley. The inequality is already sharp in the context of α-subordinate Itô processes.},
author = {Adam Osękowski},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {submartingales; semimartingales; Itō processes; weak-type inequality; differential subordination},
language = {eng},
number = {1},
pages = {73-88},
title = {A Weak-Type Inequality for Submartingales and Itô Processes},
url = {http://eudml.org/doc/281306},
volume = {63},
year = {2015},
}

TY - JOUR
AU - Adam Osękowski
TI - A Weak-Type Inequality for Submartingales and Itô Processes
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2015
VL - 63
IS - 1
SP - 73
EP - 88
AB - Let α ∈ [0,1] be a fixed parameter. We show that for any nonnegative submartingale X and any semimartingale Y which is α-subordinate to X, we have the sharp estimate $∥Y∥_{W} ≤ (2(α+1)²)/(2α+1) ∥X∥_{L^∞}$. Here W is the weak-$L^∞$ space introduced by Bennett, DeVore and Sharpley. The inequality is already sharp in the context of α-subordinate Itô processes.
LA - eng
KW - submartingales; semimartingales; Itō processes; weak-type inequality; differential subordination
UR - http://eudml.org/doc/281306
ER -

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