Acknowledgement
Supported by : NNSF of China
References
- J. A. D Appleby, Decay and growth rates of solutions of scalar stochastic delay differential equations with unbounded delay and state dependent noise, Stoch. Dyn. 5 (2005), no. 2, 133-147. https://doi.org/10.1142/S0219493705001353
- J. A. D. Appleby and E. Buckwar, Sufficient condition for polynomial asymp- totic behavier of stochastic pantograph equations, available at www.dcu.ie/maths/research/preprint.shtml.
- L. Arnold, Stochastic Differential Equations: Theory and applications, Wiley, New York, 1974.
- A. Berman and R. J. Plemmons, Nonnegative Matrices in the Mathematical Sciences, SIAM, Philadelphia, PA. 1994.
- J. Cermak, The asymptotics of solutions for a class of delay differential equations, Rocky Mountain J. Math. 33 (2003), no. 3, 775-786. https://doi.org/10.1216/rmjm/1181069927
- J. Cermak and Stanislava Dvorakova, Asymptotic estimation for some nonlinear delay differential equations, Recults Math. 51 (2008), no. 3-4, 201-213. https://doi.org/10.1007/s00025-007-0270-4
- M. L. Heard, A change of variables for functional differential equations, J. Differential Equations 18 (1975), 1-10. https://doi.org/10.1016/0022-0396(75)90076-5
- D. J. Higham, X. Mao, and C. Yuan, Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations, SIAM J. Numer. Anal. 45 (2007), no. 2, 592-609. https://doi.org/10.1137/060658138
- A. Iserles, On the generalized pantograph functional-differential equation, European J. Appl. Math. 4 (1993), no. 1, 1-38.
- R. Z. Khas'minskii, Stochastic Stability of Differential Equations, Sijthoff and Noordhoff, 1981.
- V. B. Kolmanovskii and V. R. Nosov, Stability of Functional Differential Equations, Academic Press, New York, 1986.
- G. Makay and J. Terjeki, On the asymptotic behavior of the pantograph equations, Elec- tron. J. Qual. Theory Differ. Equ. 1998 (1998), no. 2, 1-12.
- X. Mao, Exponential Stability of Stochastic Differential Equations, Dekker, 1994.
- X. Mao, Razumikhin-type theorems on exponential stability of stochastic functional differential equations, Stochastic Process, Stochastic Process. Appl. 65 (1996), no. 2, 233- 250.
- X. Mao, Razumikhin-type theorems on exponential stability of neutral stochastic functional differential equations, SIAM J. Math. Anal. 28 (1997), no. 2, 389-401. https://doi.org/10.1137/S0036141095290835
- X. Mao, Stochastic Differential Equations and Applications, Horwood, Chichester, 1997.
- X. Mao, A note on the LaSalle-type theorems for stochastic differential delay equations, J. Math. Anal. Appl. 268 (2002), no. 1, 125-142. https://doi.org/10.1006/jmaa.2001.7803
- X. Mao, LaSalle-type theorems for stochastic differential delay equations, J. Math. Anal. Appl. 236 (1999), no. 2, 350-369. https://doi.org/10.1006/jmaa.1999.6435
- X. Mao, The LaSalle-type theorems for stochastic functional differential equations, Non- linear Stud. 7 (2000), no. 2, 307-328.
- X. Mao, Stability of Stochastic Differential Equations with Respect to Semimartingales, Longman Scientific and technical, 1991.
- X. Mao, Stability and stabilisation of stochastic differential delay equations, IET Control Theory Appl. 1 (2007), no. 6, 1551-1566. https://doi.org/10.1049/iet-cta:20070006
- X. Mao, A. Matasov, and A. Piunovskiy, Stochastic differential delay equations with Markovian switching, Bernoulli 6 (2000), no. 1, 73-90. https://doi.org/10.2307/3318634
- X. Mao and M. J. Rassias, Khasminskii-type theorems for stochastic differential delay equations, Stoch. Anal. Appl. 23 (2005), no. 5, 1045-1069. https://doi.org/10.1080/07362990500118637
- X. Mao and C. Yuan, Stochastic Differential Equations with Markovian Switching, Imperial College press, 2006.
- Y. Shen, Q. Luo, and X. Mao, The improved LaSalle-type theorems for stochastic func- tional differential equations, J. Math. Anal. Appl. 318 (2006), no. 1, 134-154. https://doi.org/10.1016/j.jmaa.2005.05.026
Cited by
- The Razumikhin approach on general decay stability for neutral stochastic functional differential equations vol.350, pp.8, 2013, https://doi.org/10.1016/j.jfranklin.2013.05.025
- Lyapunov Stability of the Generalized Stochastic Pantograph Equation vol.2018, pp.2314-4785, 2018, https://doi.org/10.1155/2018/7490936