Exponential P-stability of stochastic $\nabla$-dynamic equations on disconnected sets

Abstract

The aim of this article is to consider the existence of solutions, finiteness of moments, and exponential p-stability of stochastic $\nabla$-dynamic equations on an arbitrary closed subset of $\mathbb{R}$, via Lyapunov functions. This work can be considered as a unification and generalization of works dealing with random difference and stochastic differential equations.

Keywords

• Differential operator
• dynamic equation
• exponential stability
• Ito's formula
• Lyapunov function