Convergence and stability of truncated Euler-Maruyama algorithm for stochastic proportional delay Mckean-Vlasov models with jump process

Amr Abosenna; Zhuoqi Liu

Convergence and stability of truncated Euler-Maruyama algorithm for stochastic proportional delay Mckean-Vlasov models with jump process

Numerical Analysis 2026-07-17 v1

Authors: Amr Abosenna , Zhuoqi Liu

Abstract

Stochastic Mckean-Vlasov models have a substantial importance in different fields such as finance, biology and control. This paper puts the light on stochastic proportional delay Mckean-Vlasov model with L\'evy jump where the non-jump coefficients are granted the permission to grow beyond linearity. The truncated Euler-Maruyama algorithm is then applied to our addressed model where the convergence rate and almost sure exponential stability of the aforementioned numerical algorithm are being investigated. Finally, numerical examples are presented to foster the theoretical analysis done throughout the paper

Keywords

stochastic McKean-Vlasov model proportional delay Lévy jump truncated Euler-Maruyama convergence rate exponential stability

Cite

@article{arxiv.2607.16438,
  title  = {Convergence and stability of truncated Euler-Maruyama algorithm for stochastic proportional delay Mckean-Vlasov models with jump process},
  author = {Amr Abosenna and Zhuoqi Liu},
  journal= {arXiv preprint arXiv:2607.16438},
  year   = {2026}
}