Some Results on Almost Sure Stability of Non-Autonomous Stochastic Differential Equations with Markovian Switching
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This paper studies both the non-autonomous stochastic differential equations and stochastic differential delay equations with Markovian switching. A new result on almost sure stability of stochastic differential equations is given. Moreover, we provide new conditions for tightness and almost sure stability of stochastic differential equations.
KeywordsStochastic differential delay equations Stability in distribution Itô’s formula Markov switching
Mathematics Subject Classification (2000)34K50 34K20 65C30 60J10
Author would like to thank anonymous reviewers for their valuable comments which helped to improve the manuscript. This research was supported in part by the Foundation for Science and Technology Development of Vietnam’s Ministry of Education and Training. No. B2015-27-15 and Vietnam National Foundation for Science and Technology Development (NAFOSTED) no. 101.03-2014.58. This work was finished during the author’s postdoctoral fellowship at the Vietnam Institute for Advanced Study in Mathematics (VIASM). He is grateful for the support and hospitality of VIASM.
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