On the Stability of Stochastic Dynamic Equations on Time Scales
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This paper is concerned with some sufficient conditions ensuring the stochastic stability and the almost sure exponential stability of stochastic differential equations on time scales via Lyapunov functional methods. This work can be considered as a unification and generalization of works dealing with these areas of stochastic difference and differential equations.
KeywordsDynamic equations on time scale Quadratic co-variation Martingales Itô’s formula Stochastic exponential function Lyapunov stability
Mathematics Subject Classification (2010)60H10 60J60 34A40 34D20 39A13
This research was supported in part by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.03-2017.308 and Foundation of Science and Technology Development of Vietnam’s Ministry of Education and Training under grant number B2015-27-15. This paper was revised when the second author was working as a researcher at the Vietnam Institute for Advance Study in Mathematics (VIASM). He would like to thank the VIASM for providing a fruitful research environment and extending support and hospitality during his visit.
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