A stochastic Gronwall inequality in random time horizon and its application to BSDE

Abstract In this paper, we introduce and prove a stochastic Gronwall inequality in an (unbounded) random time horizon. As an application, we prove a comparison theorem for backward stochastic differential equation (BSDE for short) with random terminal time under a stochastic monotonicity condition.

Bibliographic Details
Main Authors:	Hun O, Mun-Chol Kim, Chol-Kyu Pak
Format:	Article
Language:	English
Published:	SpringerOpen 2020-02-01
Series:	Journal of Inequalities and Applications
Subjects:	Gronwall inequality Stochastic Random time horizon Backward stochastic differential equation Comparison
Online Access:	https://doi.org/10.1186/s13660-020-2304-3

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spelling	doaj-53d61f64aeb24cfd9ceacbc4f89285c42021-02-07T12:03:39ZengSpringerOpenJournal of Inequalities and Applications1029-242X2020-02-012020111010.1186/s13660-020-2304-3A stochastic Gronwall inequality in random time horizon and its application to BSDEHun O0Mun-Chol Kim1Chol-Kyu Pak2Faculty of Mathematics, Kim Il Sung UniversityFaculty of Mathematics, Kim Il Sung UniversityFaculty of Mathematics, Kim Il Sung UniversityAbstract In this paper, we introduce and prove a stochastic Gronwall inequality in an (unbounded) random time horizon. As an application, we prove a comparison theorem for backward stochastic differential equation (BSDE for short) with random terminal time under a stochastic monotonicity condition.https://doi.org/10.1186/s13660-020-2304-3Gronwall inequalityStochasticRandom time horizonBackward stochastic differential equationComparison
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Hun O Mun-Chol Kim Chol-Kyu Pak
spellingShingle	Hun O Mun-Chol Kim Chol-Kyu Pak A stochastic Gronwall inequality in random time horizon and its application to BSDE Journal of Inequalities and Applications Gronwall inequality Stochastic Random time horizon Backward stochastic differential equation Comparison
author_facet	Hun O Mun-Chol Kim Chol-Kyu Pak
author_sort	Hun O
title	A stochastic Gronwall inequality in random time horizon and its application to BSDE
title_short	A stochastic Gronwall inequality in random time horizon and its application to BSDE
title_full	A stochastic Gronwall inequality in random time horizon and its application to BSDE
title_fullStr	A stochastic Gronwall inequality in random time horizon and its application to BSDE
title_full_unstemmed	A stochastic Gronwall inequality in random time horizon and its application to BSDE
title_sort	stochastic gronwall inequality in random time horizon and its application to bsde
publisher	SpringerOpen
series	Journal of Inequalities and Applications
issn	1029-242X
publishDate	2020-02-01
description	Abstract In this paper, we introduce and prove a stochastic Gronwall inequality in an (unbounded) random time horizon. As an application, we prove a comparison theorem for backward stochastic differential equation (BSDE for short) with random terminal time under a stochastic monotonicity condition.
topic	Gronwall inequality Stochastic Random time horizon Backward stochastic differential equation Comparison
url	https://doi.org/10.1186/s13660-020-2304-3
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A stochastic Gronwall inequality in random time horizon and its application to BSDE

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