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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The Razumikhin-type stability theorems of neutral stochastic functional differential equations (NFDEs) were investigated by several authors, but there was almost no Razumikhin-type theorems on the general asymptotic stability of NFDEs with infinite delay. This paper investigates the Razumikhin-type pth moment asymptotic stability of neutral stochastic pantograph equations (NSPEs). Sufficient conditions of the pth moment asymptotic stability for NSPEs are obtained. The NSPE is a special class of NFDEs with infinite delay. We should emphasize that the Razumikhin-type theorem of this paper is established without taking difficulties from infinite delay into account. We also develop the backward Euler method for NSPEs. We prove that the backward Euler method can preserve the asymptotic behavior of the mean square stability of exact solutions under suitable conditions. Numerical examples are demonstrated for illustration. © 2013 Yu.

Razumikhin-type theorem and mean square asymptotic behavior of the backward Euler method for neutral stochastic pantograph equations