|
|
|
General decay asymptotic stability of neutral stochastic differential delayed equations with Markov switching |
Guangqiang LAN( ), Fang XIA |
| College of Mathematics and Physics, Beijing University of Chemical Technology, Beijing 100029, China |
|
| 1 |
G Basak, A Bisi, M K Ghosh. Stability of a random diffusion with linear drift. J Math Anal Appl, 1996, 202: 604–622
https://doi.org/10.1006/jmaa.1996.0336
|
| 2 |
T Caraballo, M J Garrido-Atienza, J Real. Stochastic stabilization of differential systems with general decay rate. Systems Control Lett, 2003, 48: 397–406
https://doi.org/10.1016/S0167-6911(02)00293-1
|
| 3 |
M Ghosh, A Arapostathis, S I Marcus. Optimal control of switching diffusions with applications to flexible manufacturing systems. SIAM J Control Optim, 1993, 31: 1183–1204
https://doi.org/10.1137/0331056
|
| 4 |
L Hu, X Mao, Y Shen. Stability and boundedness of nonlinear hybrid stochastic differential delay equations. Systems Control Lett, 2013, 62: 178–187
https://doi.org/10.1016/j.sysconle.2012.11.009
|
| 5 |
L Hu, X Mao, L Zhang. Robust stability and boundedness of nonlinear hybrid stochastic differential delay equations. IEEE Trans Automat Control, 2013, 58: 2319–2332
https://doi.org/10.1109/TAC.2013.2256014
|
| 6 |
Y Hu, F Wu, C Huang. General decay pathwise stability of neutral stochastic differential equations with unbounded delay. Acta Math Sin (Engl Ser), 2011, 27: 2153–2168
https://doi.org/10.1007/s10114-011-9456-5
|
| 7 |
V Kolmanovskii, N Koroleva, T Maienberg, X Mao. Neutral stochastic differential delay equations with Markovian switching. Stoch Anal Appl, 2003, 21: 839–867
https://doi.org/10.1081/SAP-120022865
|
| 8 |
G Lan, J-L Wu. New sufficient conditions of existence, moment estimations and non confluence for SDEs with non-Lipschitzian coefficients. Stochastic Process Appl, 2014, 124: 4030–4049
https://doi.org/10.1016/j.spa.2014.07.010
|
| 9 |
G Lan, C Yuan. Exponential stability of the exact solutions and θ-EM approximations to neutral SDDEs with Markov switching. J Comput Appl Math, 2015, 285: 230–242
https://doi.org/10.1016/j.cam.2015.02.028
|
| 10 |
K Liu, A Chen. Moment decay rates of solutions of stochastic differential equations. Tohoku Math J, 2001, 53: 81–93
https://doi.org/10.2748/tmj/1178207532
|
| 11 |
L Liu, Y Shen. 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
https://doi.org/10.1002/asjc.393
|
| 12 |
X Mao. Stability of stochastic differential equations with Markovian switching. Stochastic Process Appl, 1999, 79: 45–67
https://doi.org/10.1016/S0304-4149(98)00070-2
|
| 13 |
X Mao. Stochastic Differential Equations and Applications. 2nd ed. Cambridge: Woodhead Publishing, 2007
|
| 14 |
X Mao, Y Shen, C Yuan. Almost surely asymptotic stability of neutral stochastic differential equations with Markovian switching. Stochastic Process Appl, 2008, 118: 1385–1406
https://doi.org/10.1016/j.spa.2007.09.005
|
| 15 |
X Mao, C Yuan. Stochastic Differential Equations with Markovian Switching. London: Imperial College Press, 2006
https://doi.org/10.1142/p473
|
| 16 |
M Milošević. 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
https://doi.org/10.1016/j.mcm.2012.09.016
|
| 17 |
M Obradović, M Milošević. 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
https://doi.org/10.1016/j.cam.2016.06.038
|
| 18 |
G Pavlović, S Janković. Razumikhin-type theorems on general decay stability of stochastic functional differential equations with infinite delay. J Comput Appl Math, 2012, 236: 1679–1690
https://doi.org/10.1016/j.cam.2011.09.045
|
| 19 |
G Pavlović, S Janković. The Razumikhin approach on general decay stability for neutral stochastic functional differential equations. J Franklin Inst, 2013, 350: 2124–2145
https://doi.org/10.1016/j.jfranklin.2013.05.025
|
| 20 |
R Situ. Theory of Stochastic Differential Equations with Jumps and Applications. Mathematical and Analytical Techniques with Applications to Engineering. New York: Springer, 2005
|
| 21 |
A V Skorokhod. Asymptotic Methods in the Theory of Stochastic Differential Equations. Providence: Amer Math Soc, 1989
|
| 22 |
Y Song, Q Yin, Y Shen, G Wang. Stochastic suppression and stabilization of nonlinear differential systems with general decay rate. J Franklin Inst, 2013, 350: 2084–2095
https://doi.org/10.1016/j.jfranklin.2012.11.015
|
| 23 |
F Wu, S Hu. Razumikhin-type theorems on general decay stability and robustness for stochastic functional differential equations. Internat J Robust Nonlinear Control, 2012, 22: 763–777
https://doi.org/10.1002/rnc.1726
|
| 24 |
C Yuan, J Lygeros. Stabilization of a class of stochastic differential equations with Markovian switching. Systems Control Lett, 2005, 54: 819–833
https://doi.org/10.1016/j.sysconle.2005.01.001
|
| 25 |
X Zong, F Wu, C Huang. 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
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
| |
Shared |
|
|
|
|
| |
Discussed |
|
|
|
|
