Well-posedness and approximation of some one-dimensional Lévy-driven non-linear SDEs

Noufel Frikha and Libo Li

Stochastic Processes and their Applications, 2021, vol. 132, issue C, 76-107

Abstract: In this article, we are interested in the strong well-posedness together with the numerical approximation of some one-dimensional stochastic differential equations with a non-linear drift, in the sense of McKean–Vlasov, driven by a spectrally-positive Lévy process and a Brownian motion. We provide criteria for the existence of strong solutions under non-Lipschitz conditions of Yamada–Watanabe type without non-degeneracy assumption following the approach developed by Li and Mytnik (2011). The strong convergence rate of the propagation of chaos for the associated particle system and of the corresponding Euler–Maruyama scheme are also investigated. In particular, the strong convergence rate of the Euler–Maruyama scheme exhibits an interplay between the regularity of the coefficients and the order of singularity of the Lévy measure around zero.

Keywords: McKean–Vlasov SDEs; Lévy driven SDEs; Strong uniqueness; Propagation of chaos (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414920303926
Full text for ScienceDirect subscribers only

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:eee:spapps:v:132:y:2021:i:c:p:76-107

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.spa.2020.10.002

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().