Moment Inequality for the Martingale Square Function
Bulletin of the Polish Academy of Sciences. Mathematics (2013)
- Volume: 61, Issue: 2, page 169-180
- ISSN: 0239-7269
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topAdam Osękowski. "Moment Inequality for the Martingale Square Function." Bulletin of the Polish Academy of Sciences. Mathematics 61.2 (2013): 169-180. <http://eudml.org/doc/281152>.
@article{AdamOsękowski2013,
abstract = {Consider the sequence $(Cₙ)_\{n≥1\}$ of positive numbers defined by C₁ = 1 and $C_\{n+1\} = 1 + Cₙ²/4$, n = 1,2,.... Let M be a real-valued martingale and let S(M) denote its square function. We establish the bound
|Mₙ|≤ Cₙ Sₙ(M), n=1,2,...,
and show that for each n, the constant Cₙ is the best possible.},
author = {Adam Osękowski},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
keywords = {martingales; sum of squares of the increments; method of moments; best constants},
language = {eng},
number = {2},
pages = {169-180},
title = {Moment Inequality for the Martingale Square Function},
url = {http://eudml.org/doc/281152},
volume = {61},
year = {2013},
}
TY - JOUR
AU - Adam Osękowski
TI - Moment Inequality for the Martingale Square Function
JO - Bulletin of the Polish Academy of Sciences. Mathematics
PY - 2013
VL - 61
IS - 2
SP - 169
EP - 180
AB - Consider the sequence $(Cₙ)_{n≥1}$ of positive numbers defined by C₁ = 1 and $C_{n+1} = 1 + Cₙ²/4$, n = 1,2,.... Let M be a real-valued martingale and let S(M) denote its square function. We establish the bound
|Mₙ|≤ Cₙ Sₙ(M), n=1,2,...,
and show that for each n, the constant Cₙ is the best possible.
LA - eng
KW - martingales; sum of squares of the increments; method of moments; best constants
UR - http://eudml.org/doc/281152
ER -
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