Tamed EM schemes for neutral stochastic differential delay equations with superlinear diffusion coefficients

Shounian Deng, Chen Fei, Weiyin Fei, Xuerong Mao

Research output: Contribution to journalArticle

Abstract

In this article, we propose two types of explicit tamed Euler-Maruyama (EM) schemes for neutral stochastic differential delay equations with super linearly growing drift and diffusion coefficients. The first type is convergent in the Lq sense under the local Lipschitz plus Khasminskii-type conditions. The second type is of order half in the mean-square sense under the Khasminskii-type, global monotonicity and polynomial growth conditions. Moreover, it is proved that the partially tamed EM scheme has the property of mean-square exponential stability. Numerical examples are provided to illustrate the theoretical findings.
Original languageEnglish
Number of pages33
JournalJournal of Computational and Applied Mathematics
Publication statusAccepted/In press - 2 Nov 2020

Keywords

  • neutral stochastic differential delay equation
  • tamed EM scheme
  • super-linear growth
  • strong convergence
  • mean square stability

Fingerprint Dive into the research topics of 'Tamed EM schemes for neutral stochastic differential delay equations with superlinear diffusion coefficients'. Together they form a unique fingerprint.

Cite this