Stability of hybrid pantograph stochastic functional differential equations

TL;DR

This paper introduces hybrid pantograph stochastic functional differential equations and analyzes their stability properties using Lyapunov methods, providing insights into their moment and sample behaviors.

Contribution

It presents a novel class of stochastic differential equations and investigates their stability characteristics, expanding understanding of their dynamic properties.

Findings

Established moment exponential stability.

Proved almost sure exponential stability.

Demonstrated almost sure polynomial stability.

Abstract

In this paper, we study a new type of stochastic functional differential equations which is called hybrid pantograph stochastic functional differential equations. We investigate several moment properties and sample properties of the solutions to the equations by using the method of multiple Lyapunov functions, such as the moment exponential stability, almost sure exponential stability and almost sure polynomial stability, etc.