English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper mainly investigates the strong convergence and stability of thetruncated Euler-Maruyama (EM) method for stochastic differential delayequations with variable delay whose coefficients can be growing super-linearly.By constructing appropriate truncated functions to control the super-lineargrowth of the original coefficients, we present a type of the truncated EMmethod for such SDDEs with variable delay, which is proposed to be approximatedby the value taken at the nearest grid points on the left of the delayedargument. The strong convergence result (without order) of the method isestablished under the local Lipschitz plus generalized Khasminskii-typeconditions and the optimal strong convergence order $1/2$ can be obtained ifthe global monotonicity with U function and polynomial growth conditions areadded to the assumptions. Moreover, the partially truncated EM method is provedto preserve the mean-square and H_\infty stabilities of the true solutions.Compared with the known results on the truncated EM method for SDDEs, a betterorder of strong convergence is obtained under more relaxing conditions on thecoefficients, and more refined technical estimates are developed so as toovercome the challenges arising due to variable delay. Lastly, some numericalexamples are utilized to confirm the effectiveness of the theoretical results.

The truncated EM method for stochastic differential delay equations with variable delay