Sharp moment estimates for martingales with uniformly bounded square functions

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Sharp moment estimates for martingales with uniformly bounded square functions. / Stolyarov, Dmitriy ; Vasyunin, Vasily ; Zatitskiy, Pavel; Zlotnikov, Ilya.

In: Mathematische Zeitschrift, Vol. 302, No. 1, 01.09.2022, p. 181-217.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{6e88c3e0ebf74f0aa556ce1fe02a3168,

title = "Sharp moment estimates for martingales with uniformly bounded square functions",

abstract = "We provide sharp bounds for the exponential moments and p-moments, 1 ≤ p≤ 2 , of the terminate distribution of a martingale whose square function is uniformly bounded by one. We introduce a Bellman function for the corresponding extremal problem and reduce it to the already known Bellman function on BMO ([0 , 1]). In the case of tail estimates, a similar reduction does not work exactly, so we come up with a fine supersolution that leads to sharp tail estimates.",

keywords = "Bellman function, Burkholder method, Martingale, Square function",

author = "Dmitriy Stolyarov and Vasily Vasyunin and Pavel Zatitskiy and Ilya Zlotnikov",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2022",

month = sep,

day = "1",

doi = "10.1007/s00209-022-03064-x",

language = "English",

volume = "302",

pages = "181--217",

journal = "Mathematische Zeitschrift",

issn = "0025-5874",

publisher = "Springer Nature",

number = "1",

}

RIS

TY - JOUR

T1 - Sharp moment estimates for martingales with uniformly bounded square functions

AU - Stolyarov, Dmitriy

AU - Vasyunin, Vasily

AU - Zatitskiy, Pavel

AU - Zlotnikov, Ilya

PY - 2022/9/1

Y1 - 2022/9/1

N2 - We provide sharp bounds for the exponential moments and p-moments, 1 ≤ p≤ 2 , of the terminate distribution of a martingale whose square function is uniformly bounded by one. We introduce a Bellman function for the corresponding extremal problem and reduce it to the already known Bellman function on BMO ([0 , 1]). In the case of tail estimates, a similar reduction does not work exactly, so we come up with a fine supersolution that leads to sharp tail estimates.

AB - We provide sharp bounds for the exponential moments and p-moments, 1 ≤ p≤ 2 , of the terminate distribution of a martingale whose square function is uniformly bounded by one. We introduce a Bellman function for the corresponding extremal problem and reduce it to the already known Bellman function on BMO ([0 , 1]). In the case of tail estimates, a similar reduction does not work exactly, so we come up with a fine supersolution that leads to sharp tail estimates.

KW - Bellman function

KW - Burkholder method

KW - Martingale

KW - Square function

UR - http://www.scopus.com/inward/record.url?scp=85132147304&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/2e96df85-a314-3a6b-bc5e-c801118e3ed9/

U2 - 10.1007/s00209-022-03064-x

DO - 10.1007/s00209-022-03064-x

M3 - Article

AN - SCOPUS:85132147304

VL - 302

SP - 181

EP - 217

JO - Mathematische Zeitschrift

JF - Mathematische Zeitschrift

SN - 0025-5874

IS - 1

ER -

ID: 99965297