On the practical global uniform asymptotic stability of stochastic differential equations. Issue 1 (2nd January 2016)

• Record Type: Journal Article
• Authors: Caraballo, Tomás; Hammami, Mohamed Ali; Mchiri, Lassaad
• Is Part Of: Stochastics. Volume 88:Issue 1(2016)
• Page Start: 45
• Page End: 56
• Publication Date: 2016-01-02
• Subjects: stochastic differential equations -- Lyapunov techniques -- practical asymptotic stability; Stochastic processes -- Periodicals; Probabilities -- Periodicals; 519.2
• DOI: 10.1080/17442508.2015.1029719
• Languages: English
• ISSNs: 1744-2508

Abstract

Abstract : The method of Lyapunov functions is one of the most effective ones for the investigation of stability of dynamical systems, in particular, of stochastic differential systems. The main purpose of the paper is the analysis of the stability of stochastic differential equations (SDEs) by using Lyapunov functions when the origin is not necessarily an equilibrium point. The global uniform boundedness and the global practical uniform exponential stability of solutions of SDEs based on Lyapunov techniques are investigated. Furthermore, an example is given to illustrate the applicability of the main result.