Almost sure stability with general decay rate of neutral stochastic pantograph equations with Markovian switching

Abstract

This paper focuses on the general decay stability of nonlinear neutral stochastic pantograph equations with Markovian switching (NSPEwMSs). Under the local Lipschitz condition and non-linear growth condition, the existence and almost sure stability with general decay of the solution for NSPEwMSs are investigated. By means of M-matrix theory, some sufficient conditions on the general decay stability are also established for NSPEwMSs.

Keywords

• neutral stochastic pantograph equations
• markovian switching
• existence and uniqueness results
• general decay stability