RESEARCH ARTICLE

General decay asymptotic stability of neutral stochastic differential delayed equations with Markov switching

  • Guangqiang LAN ,
  • Fang XIA
Expand
  • College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China

Received date: 02 Mar 2018

Accepted date: 28 Jul 2019

Published date: 15 Aug 2019

Copyright

2019 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature

Abstract

The p-th moment and almost sure stability with general decay rate of the exact solutions of neutral stochastic differential delayed equations with Markov switching are investigated under given conditions. Two examples are provided to support the conclusions.

Cite this article

Guangqiang LAN , Fang XIA . General decay asymptotic stability of neutral stochastic differential delayed equations with Markov switching[J]. Frontiers of Mathematics in China, 2019 , 14(4) : 793 -818 . DOI: 10.1007/s11464-019-0781-9

1
Basak G, Bisi A, Ghosh M K. Stability of a random diffusion with linear drift. J Math Anal Appl, 1996, 202: 604–622

DOI

2
Caraballo T, Garrido-Atienza M J, Real J. Stochastic stabilization of differential systems with general decay rate. Systems Control Lett, 2003, 48: 397–406

DOI

3
Ghosh M, Arapostathis A, Marcus S I. Optimal control of switching diffusions with applications to flexible manufacturing systems. SIAM J Control Optim, 1993, 31: 1183–1204

DOI

4
Hu L, Mao X, Shen Y. Stability and boundedness of nonlinear hybrid stochastic differential delay equations. Systems Control Lett, 2013, 62: 178–187

DOI

5
Hu L, Mao X, Zhang L. Robust stability and boundedness of nonlinear hybrid stochastic differential delay equations. IEEE Trans Automat Control, 2013, 58: 2319–2332

DOI

6
Hu Y, Wu F, Huang C. General decay pathwise stability of neutral stochastic differential equations with unbounded delay. Acta Math Sin (Engl Ser), 2011, 27: 2153–2168

DOI

7
Kolmanovskii V, Koroleva N, Maienberg T, Mao X. Neutral stochastic differential delay equations with Markovian switching. Stoch Anal Appl, 2003, 21: 839–867

DOI

8
Lan G, Wu J-L. New sufficient conditions of existence, moment estimations and non confluence for SDEs with non-Lipschitzian coefficients. Stochastic Process Appl, 2014, 124: 4030–4049

DOI

9
Lan G, Yuan C. Exponential stability of the exact solutions and θ-EM approximations to neutral SDDEs with Markov switching. J Comput Appl Math, 2015, 285: 230–242

DOI

10
Liu K, Chen A. Moment decay rates of solutions of stochastic differential equations. Tohoku Math J, 2001, 53: 81–93

DOI

11
Liu L, Shen Y. The almost sure asymptotic stability and pth moment asymptotic stability of nonlinear stochastic delay differential systems with polynomial growth. Asian J Control, 2012, 14: 859–867

DOI

12
Mao X. Stability of stochastic differential equations with Markovian switching. Stochastic Process Appl, 1999, 79: 45–67

DOI

13
Mao X. Stochastic Differential Equations and Applications. 2nd ed. Cambridge: Woodhead Publishing, 2007

14
Mao X, Shen Y, Yuan C. Almost surely asymptotic stability of neutral stochastic differential equations with Markovian switching. Stochastic Process Appl, 2008, 118: 1385–1406

DOI

15
Mao X, Yuan C. Stochastic Differential Equations with Markovian Switching. London: Imperial College Press, 2006

DOI

16
Milošević M. Almost sure exponential stability of solutions to highly nonlinear neutral stochastic differential equations with time-dependent delay and the Euler-Maruyama approximation. Math Comput Modelling, 2013, 57: 887–899

DOI

17
Obradović M, Milošević M. Stability of a class of neutral stochastic differential equations with unbounded delay and Markovian switching and the Euler-Maruyama method. J Comput Appl Math, 2017, 309: 244–266

DOI

18
Pavlović G, Janković S. Razumikhin-type theorems on general decay stability of stochastic functional differential equations with infinite delay. J Comput Appl Math, 2012, 236: 1679–1690

DOI

19
Pavlović G, Janković S. The Razumikhin approach on general decay stability for neutral stochastic functional differential equations. J Franklin Inst, 2013, 350: 2124–2145

DOI

20
Situ R. Theory of Stochastic Differential Equations with Jumps and Applications. Mathematical and Analytical Techniques with Applications to Engineering. New York: Springer, 2005

21
Skorokhod A V. Asymptotic Methods in the Theory of Stochastic Differential Equations. Providence: Amer Math Soc, 1989

22
Song Y, Yin Q, Shen Y, Wang G. Stochastic suppression and stabilization of nonlinear differential systems with general decay rate. J Franklin Inst, 2013, 350: 2084–2095

DOI

23
Wu F, Hu S. Razumikhin-type theorems on general decay stability and robustness for stochastic functional differential equations. Internat J Robust Nonlinear Control, 2012, 22: 763–777

DOI

24
Yuan C, Lygeros J. Stabilization of a class of stochastic differential equations with Markovian switching. Systems Control Lett, 2005, 54: 819–833

DOI

25
Zong X, Wu F, Huang C. The boundedness and exponential stability criterions for nonlinear hybrid neutral stochastic functional differential equations. Abstr Appl Anal, 2013, Article ID 138031, 12 pp, https://doi.org/10.1155/2013/138031

DOI

Outlines

/