Stability analysis of time-varying neutral stochastic pantograph equations with Markovian switching and multiple proportional delays

This paper rigorously investigates the stochastic stability of time-varying neutral stochastic pantograph systems with Markovian switching. Primarily, multiple proportional delays and time-varying coefficients are taken into account in the neutral hybrid stochastic systems. In order to surmount the complexities stemming from those factors, the Lyapunov functional approach and several stochastic analytical techniques are utilized, and a modified version of pantograph delays integral inequality is developed. Moreover, various stability criteria such as $ q $th moment stability, $ q $th moment asymptotic stability, $ q $th exponential stability, almost sure asymptotic stability and almost sure exponential stability are put forward, where the upper bound of the diffusion operator can be a function with sign-changed time-varying coefficients rather than negative constants. Eventually, through several numerical examples, the theoretical results are strictly verified, demonstrating the feasibility and effectiveness of the proposed method.