Infinite time interval backward stochastic differential equations with continuous coefficients

In this paper, we study the existence theorem for [Formula: see text] [Formula: see text] solutions to a class of 1-dimensional infinite time interval backward stochastic differential equations (BSDEs) under the conditions that the coefficients are continuous and have linear growths. We also obtain...

Descripción completa

Detalles Bibliográficos
Autores principales: Zong, Zhaojun, Hu , Feng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2016
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5053973/
https://www.ncbi.nlm.nih.gov/pubmed/27795882
http://dx.doi.org/10.1186/s40064-016-3419-3
_version_ 1782458497803223040
author Zong, Zhaojun
Hu , Feng
author_facet Zong, Zhaojun
Hu , Feng
author_sort Zong, Zhaojun
collection PubMed
description In this paper, we study the existence theorem for [Formula: see text] [Formula: see text] solutions to a class of 1-dimensional infinite time interval backward stochastic differential equations (BSDEs) under the conditions that the coefficients are continuous and have linear growths. We also obtain the existence of a minimal solution. Furthermore, we study the existence and uniqueness theorem for [Formula: see text] [Formula: see text] solutions of infinite time interval BSDEs with non-uniformly Lipschitz coefficients. It should be pointed out that the assumptions of this result is weaker than that of Theorem 3.1 in Zong (Turkish J Math 37:704–718, 2013).
format Online
Article
Text
id pubmed-5053973
institution National Center for Biotechnology Information
language English
publishDate 2016
publisher Springer International Publishing
record_format MEDLINE/PubMed
spelling pubmed-50539732016-10-28 Infinite time interval backward stochastic differential equations with continuous coefficients Zong, Zhaojun Hu , Feng Springerplus Research In this paper, we study the existence theorem for [Formula: see text] [Formula: see text] solutions to a class of 1-dimensional infinite time interval backward stochastic differential equations (BSDEs) under the conditions that the coefficients are continuous and have linear growths. We also obtain the existence of a minimal solution. Furthermore, we study the existence and uniqueness theorem for [Formula: see text] [Formula: see text] solutions of infinite time interval BSDEs with non-uniformly Lipschitz coefficients. It should be pointed out that the assumptions of this result is weaker than that of Theorem 3.1 in Zong (Turkish J Math 37:704–718, 2013). Springer International Publishing 2016-10-06 /pmc/articles/PMC5053973/ /pubmed/27795882 http://dx.doi.org/10.1186/s40064-016-3419-3 Text en © The Author(s) 2016 Open AccessThis 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
Zong, Zhaojun
Hu , Feng
Infinite time interval backward stochastic differential equations with continuous coefficients
title Infinite time interval backward stochastic differential equations with continuous coefficients
title_full Infinite time interval backward stochastic differential equations with continuous coefficients
title_fullStr Infinite time interval backward stochastic differential equations with continuous coefficients
title_full_unstemmed Infinite time interval backward stochastic differential equations with continuous coefficients
title_short Infinite time interval backward stochastic differential equations with continuous coefficients
title_sort infinite time interval backward stochastic differential equations with continuous coefficients
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5053973/
https://www.ncbi.nlm.nih.gov/pubmed/27795882
http://dx.doi.org/10.1186/s40064-016-3419-3
work_keys_str_mv AT zongzhaojun infinitetimeintervalbackwardstochasticdifferentialequationswithcontinuouscoefficients
AT hufeng infinitetimeintervalbackwardstochasticdifferentialequationswithcontinuouscoefficients

Ejemplares similares