A class of stochastic Gronwall’s inequality and its application

This paper puts forward the basic form of stochastic Gronwall’s inequality and uses, respectively, the iterative method, the integral method and the martingale representation method to prove it. Then it presents an application to prove a comparison theorem of [Formula: see text] solutions for one-di...

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Detalles Bibliográficos
Autores principales: Wang, Xin, Fan, Shengjun
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2018
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6290671/
https://www.ncbi.nlm.nih.gov/pubmed/30839903
http://dx.doi.org/10.1186/s13660-018-1932-3
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author Wang, Xin
Fan, Shengjun
author_facet Wang, Xin
Fan, Shengjun
author_sort Wang, Xin
collection PubMed
description This paper puts forward the basic form of stochastic Gronwall’s inequality and uses, respectively, the iterative method, the integral method and the martingale representation method to prove it. Then it presents an application to prove a comparison theorem of [Formula: see text] solutions for one-dimensional backward stochastic differential equations under the stochastic Lipschitz condition.
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spelling pubmed-62906712018-12-27 A class of stochastic Gronwall’s inequality and its application Wang, Xin Fan, Shengjun J Inequal Appl Research This paper puts forward the basic form of stochastic Gronwall’s inequality and uses, respectively, the iterative method, the integral method and the martingale representation method to prove it. Then it presents an application to prove a comparison theorem of [Formula: see text] solutions for one-dimensional backward stochastic differential equations under the stochastic Lipschitz condition. Springer International Publishing 2018-12-10 2018 /pmc/articles/PMC6290671/ /pubmed/30839903 http://dx.doi.org/10.1186/s13660-018-1932-3 Text en © The Author(s) 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Wang, Xin
Fan, Shengjun
A class of stochastic Gronwall’s inequality and its application
title A class of stochastic Gronwall’s inequality and its application
title_full A class of stochastic Gronwall’s inequality and its application
title_fullStr A class of stochastic Gronwall’s inequality and its application
title_full_unstemmed A class of stochastic Gronwall’s inequality and its application
title_short A class of stochastic Gronwall’s inequality and its application
title_sort class of stochastic gronwall’s inequality and its application
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6290671/
https://www.ncbi.nlm.nih.gov/pubmed/30839903
http://dx.doi.org/10.1186/s13660-018-1932-3
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