LAUSR

This study investigates the stability of a class of neutral stochastic functional differential equations with Markovian switching. Some novel stability criteria are first established, including boundedness, pth moment exponential stability and almost sure exponential stability, based on multiple Lyapunov functions, generalised Ito formula and non-negative semi-martingale convergence theorem. Concretely, the authors generalise the existing results under the essential neutral term and improve the diffusion operators from being controlled by two auxiliary functions to other multiple auxiliary functions with not only constant coefficients but also time-varying coefficients. Some numerical examples are presented to illustrate the effectiveness of the obtained results.