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Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 15
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Articles

Stability of neutral stochastic functional differential equations with Markovian switching driven by G-Brownian motion

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Pages 2555-2572 | Received 31 Oct 2016, Accepted 05 Sep 2017, Published online: 20 Sep 2017

References

  • Mao X . Razumikhin-type theorems on exponential stability of neutral stochastic functional differential equations. SIAM J Math Anal. 1997;28:389–401.
  • Zhao X , Deng F . A new type of stability theorem for stochastic systems with application to stochastic stabilization. IEEE Trans Automat Control. 2016;61:240–245.
  • Huang Z , Yang Q , Cao J . Stochastic stability and bifurcation for the chronic state in Marchuk’s model with noise. Appl Math Model. 2011;35:5842–5855.
  • Huang Z , Yang QG , Cao J . Stochastic stability and bifurcation analysis on Hopfield neural networks with noise. Expert Syst Appl. 2011;38:10437–10445.
  • Zhu Q , Cao J . Stability analysis of Markovian jump stochastic BAM neural networks with impulse control and mixed time delays. IEEE Trans Neural Netw Learn. Syst. 2012;23:467–479.
  • Hale JK , Meyer KR . A class of functional equations of neutral type. Mem Amer Math Soc. 1967;76:1–65.
  • Kolmanovskii V , Myshkis A . Applied theory of functional differential equations. Dordrecht: kluwer Academic publisher; 1992.
  • Kolmanovskii VB , Nosov VR . Stability and periodic modes of control systems with aftereffect. Moscow: Nauka; 1981.
  • Mao X . Stochastic differential equations and applications. Chichester: Horwood Publication; 1997.
  • Randjelović J , Janković S . On the pth moment exponential stability criteria of neutral stochastic functional differential equations. J Math Anal Appl. 2007;326:266–280.
  • Janković S , Jovanović M . The p-th moment exponential stability of neutral stochastic functional differential equations. Filomat. 2006;20:59–72.
  • Huang L , Deng F . Razumikhin-type theorems on stability of neutral stochastic functional differential equations. IEEE Trans Automat Control. 2008;53:1718–1723.
  • Janković S , Randjelović J , Jovanović M . Razumikhin-type exponential stability criteria of neutral stochastic functional differential equations. J Math Anal Appl. 2009;355:811–820.
  • Kolmanovskii V , Koroleva N , Maizenberg T , et al . Neutral stochastic differential delay equations with Markovian switching. Stoch Anal Appl. 2003;21:819–847.
  • Mao X , Yuan C . Stochastic differential equations with Markovian switching. London: Imperial College Press; 2006.
  • Zhu Q , Cao J . Exponential stability of stochastic neural networks with both Markovian jump parameters and mixed time delays. IEEE Trans Syst Man Cybern B. 2011;41:341–353.
  • Zhu Q , Cao J . Stability of Markovian jump neural networks with impulse control and time varying delays. Nonlinear Anal Real World Appl. 2012;13:2259–2270.
  • Zhu Q . pth moment exponential stability of impulsive stochastic functional differential equations with Markovian switching. J Franklin Inst. 2014;351:3965–3986.
  • Feng L , Li S , Mao X . Asymptotic stability and boundedness of stochastic functional differential equations with Markovian switching. J Franklin Inst. 2016;353:4924–4949.
  • Du NH , Dang NH , Dieu NT . On stability in distribution of stochastic differential delay equations with Markovian switching. Syst Control Lett. 2014;65:43–49.
  • Mao X , Shen Y , Yuan C . Almost surely asymptotic stability of neutral stochastic differential delay equations with Markovian switching. Stoch Process Appl. 2008;118:1385–1406.
  • Jao B , Hou Z , Yuan C . Stability in distribution of neutral stochastic differential delay equations with Markovian switching. Stat Probab Lett. 2009;79:1663–1673.
  • Zhou S , Hu S . Razumikhin-type theorems of neutral stochastic functional differential equations. Acta Math Sci Ser B. 2009;29:181–190.
  • Hu G , Wang K . Stability in distribution of neutral stochastic functional differential equations with Markovian switching. J Math Anal Appl. 2012;385:757–769.
  • Li X , Mao X . A note on almost sure asymptotic stability of neutral stochastic delay differential equations with Markovian switching. Automatica. 2012;48:2329–2334.
  • Xu Y , He Z . Exponential stability of neutral stochastic delay differential equations with Markovian switching. Appl Math Lett. 2016;52:64–73.
  • Peng S . G-expectation, G-Brownian motion and related stochastic calculus of Itô type. In: Benth FE , Di Nunno G , Lindstrom T , et al. , editors. Stochastic analysis and applications. The Able Symposium 2005, Abel Symposia 2. Berlin Heidelberg; 2007. p. 541–567.
  • Peng S . G-Brownian motion and dynamic risk measure under volatility uncertainty, arXiv:0711.2834. Forthcoming 2007.
  • Peng S . Multi-dimensional G-Brownian motion and related stochastic calculus under G-expectation. Stoch Process Appl. 2008;118:2223–2253.
  • Hu M , Peng S . On representation theorem of G-expectations and paths of G-Brownian motion. Acta Math Appl Sin Engl Ser. 2009;25:539–546.
  • Hu L , Ren Y , Xu T . p-Moment stability of solutions to stochastic differential equations driven by G-Brownian motion. Appl Math Comput. 2014;230:231–237.
  • Ren Y , Jia X , Hu L . Exponential stability of solutions to impulsive stochastic differential equations driven by G-Brownian motion. Discrete Contin Dyn Syst Ser B. 2015;20:2157–2169.
  • Zhang D , Chen Z . Stability theorem for stochastic differential equations driven by G-Brownian motion. ArXiv:1105.4222. Forthcoming 2011.
  • Zhang D , Chen Z . Exponential stability for stochastic differential equation driven by G-Brownian motion. Appl Math Lett. 2012;25:1906–1910.
  • Fei W , Fei C . On exponential stability for stochastic differential equations disturbed by G-Brownian motion. ArXiv:1311.7311. Forthcoming 2013.
  • Ren Y , Jia X , Sakthivel R . The p-th moment stability of solutions to impulsive stochastic differential equations driven by G-Brownian motion. Appl Anal. 2017;96:988–1003.
  • Peng S . Nonlinear expectations and stochastic calculus under uncertainty. ArXiv:1002.4546. Forthcoming 2010.
  • Li X , Peng S . Stopping times and related Itô’s calculus with G-Brownian motion. Stoch Process Appl. 2011;121:1492–1508.
  • Denis L , Hu M , Peng S . Function spaces and capacity related to a sublinear expectation: application to G-Brownian motion paths. Potential Anal. 2011;34:139–161.
  • Ren Y , Bi Q , Sakthivel R . Stochastic functional differential equations with infinite delay driven by G-Brownian motion. Math Methods Appl. Sci. 2013;36:1746–1759.
  • Bai X , Lin Y . On the existence and uniqueness of solutions to stochastic differential equations driven by G-Brownian motion with integral-Lipschitz coefficients. Acta Math Appl Sin Engl Ser. 2014;30:589–610.
  • Li X , Lin X , Lin Y . Lyapunov-type conditions and stochastic differential equations driven by G-Brownian motion. J Math Anal Appl. 2016;439:235–255.
  • Anderson WJ . Continuous-time Markov chains. Berlin: Springer; 1991.

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