Maximal inequalities and exponential estimates for stochastic convolutions driven by Levy-type processes in Banach spaces with application to stochastic quasi-geostrophic equations

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Maximal inequalities and exponential estimates for stochastic convolutions driven by Levy-type processes in Banach spaces with application to stochastic quasi-geostrophic equations. / Brzezniak, Zdzislaw; Zhu, Jiahui; Liu, Wei.

In: SIAM journal on mathematical analysis, 23.05.2019, p. 2121–2167.

Research output: Contribution to journalArticle

Harvard

Brzezniak, Z, Zhu, J & Liu, W 2019, 'Maximal inequalities and exponential estimates for stochastic convolutions driven by Levy-type processes in Banach spaces with application to stochastic quasi-geostrophic equations', SIAM journal on mathematical analysis, pp. 2121–2167. https://doi.org/10.1137/18M1169011

APA

Brzezniak, Z., Zhu, J., & Liu, W. (2019). Maximal inequalities and exponential estimates for stochastic convolutions driven by Levy-type processes in Banach spaces with application to stochastic quasi-geostrophic equations. SIAM journal on mathematical analysis, 2121–2167. https://doi.org/10.1137/18M1169011

Vancouver

Brzezniak Z, Zhu J, Liu W. Maximal inequalities and exponential estimates for stochastic convolutions driven by Levy-type processes in Banach spaces with application to stochastic quasi-geostrophic equations. SIAM journal on mathematical analysis. 2019 May 23;2121–2167. https://doi.org/10.1137/18M1169011

Author

Brzezniak, Zdzislaw ; Zhu, Jiahui ; Liu, Wei. / Maximal inequalities and exponential estimates for stochastic convolutions driven by Levy-type processes in Banach spaces with application to stochastic quasi-geostrophic equations. In: SIAM journal on mathematical analysis. 2019 ; pp. 2121–2167.

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@article{81ca10bbac6345279e1493c183a37b9e,
title = "Maximal inequalities and exponential estimates for stochastic convolutions driven by Levy-type processes in Banach spaces with application to stochastic quasi-geostrophic equations",
abstract = "We present remarkably simple proofs of Burkholder–Davis–Gundy inequalities forstochastic integrals and maximal inequalities for stochastic convolutions in Banach spaces driven by Levy-type processes. Exponential estimates for stochastic convolutions are obtained and two versionsof Ito{\textquoteright}s formula in Banach spaces are also derived. Based on the obtained maximal inequality, the existence and uniqueness of mild solutions of stochastic quasi-geostrophic equation with Levy noise is established.",
keywords = "Burkholder–Davis–Gundy inequality, maximal inequality, exponential estimate, stochastic convolution, Itˆo formula, martingale type r Banach space",
author = "Zdzislaw Brzezniak and Jiahui Zhu and Wei Liu",
note = "This is an author-produced version of the published paper. Uploaded in accordance with the publisher{\textquoteright}s self-archiving policy. Further copying may not be permitted; contact the publisher for details. ",
year = "2019",
month = may,
day = "23",
doi = "10.1137/18M1169011",
language = "English",
pages = "2121–2167",
journal = "SIAM journal on mathematical analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics Publications",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Maximal inequalities and exponential estimates for stochastic convolutions driven by Levy-type processes in Banach spaces with application to stochastic quasi-geostrophic equations

AU - Brzezniak, Zdzislaw

AU - Zhu, Jiahui

AU - Liu, Wei

N1 - This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

PY - 2019/5/23

Y1 - 2019/5/23

N2 - We present remarkably simple proofs of Burkholder–Davis–Gundy inequalities forstochastic integrals and maximal inequalities for stochastic convolutions in Banach spaces driven by Levy-type processes. Exponential estimates for stochastic convolutions are obtained and two versionsof Ito’s formula in Banach spaces are also derived. Based on the obtained maximal inequality, the existence and uniqueness of mild solutions of stochastic quasi-geostrophic equation with Levy noise is established.

AB - We present remarkably simple proofs of Burkholder–Davis–Gundy inequalities forstochastic integrals and maximal inequalities for stochastic convolutions in Banach spaces driven by Levy-type processes. Exponential estimates for stochastic convolutions are obtained and two versionsof Ito’s formula in Banach spaces are also derived. Based on the obtained maximal inequality, the existence and uniqueness of mild solutions of stochastic quasi-geostrophic equation with Levy noise is established.

KW - Burkholder–Davis–Gundy inequality

KW - maximal inequality

KW - exponential estimate

KW - stochastic convolution

KW - Itˆo formula

KW - martingale type r Banach space

U2 - 10.1137/18M1169011

DO - 10.1137/18M1169011

M3 - Article

SP - 2121

EP - 2167

JO - SIAM journal on mathematical analysis

JF - SIAM journal on mathematical analysis

SN - 0036-1410

ER -