Lyapunov functionals vs Lyapunov functions for various types of stability of hybrid stochastic differential equation

Abstract

In this paper, the effects of using Lyapunov like-functionals vs using Lyapunov like-functions coupled with partial differential inequalities on various types of stability criteria of hybrid stochastic parabolic differential equation of Itô type are investigated. A concluding remark will highlight the advantages of using the two approaches and the major differences between the utilization of two approaches for this specific type of differential equations with diffusion term.