Existence, Uniqueness and Stability of $$L^1$$ L 1 Solutions for Multidimensional Backward Stochastic Differential Equations with Generators of One-Sided Osgood Type

Sheng Jun Fan ()
Additional contact information
Sheng Jun Fan: China University of Mining and Technology

Journal of Theoretical Probability, 2018, vol. 31, issue 3, 1860-1899

Abstract: Abstract We establish a general existence and uniqueness result of $$L^1$$ L 1 solution for a multidimensional backward stochastic differential equation (BSDE for short) with generator g satisfying a one-sided Osgood condition as well as a general growth condition in y, and a Lipschitz condition together with a sublinear growth condition in z, which improves some existing results. In particular, we put forward and prove a stability theorem of the $$L^1$$ L 1 solutions for the first time. A new type of $$L^1$$ L 1 solution is also investigated. Some delicate techniques involved in the relationship between convergence in $$L^1$$ L 1 and in probability and dividing appropriately the time interval play crucial roles in our proofs.

Keywords: Backward stochastic differential equation; $$L^1$$ L 1 solution; Existence and uniqueness; Stability theorem; One-sided Osgood condition; 60H10 (search for similar items in EconPapers)
Date: 2018
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10959-017-0755-3 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:31:y:2018:i:3:d:10.1007_s10959-017-0755-3

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-017-0755-3

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().