On the general decay stability of stochastic differential equations with unbounded delay
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
This work focuses on the general decay stability of nonlinear stochastic differential equations with unbounded delay. A Razumikhin-type theorem is rst established to obtain the moment stability but with-out almost sure stability. Then an improved edition is presented to derive not only the moment stability but also the almost sure stability, while ex-isting Razumikhin-type theorems aim at only the moment stability. By virtue of the M-matrix techniques, we further develop the aforementioned Razumikhin-type theorems to be easily implementable. Two examples are given for illustration.
Abstract
This work focuses on the general decay stability of nonlinear stochastic differential equations with unbounded delay. A Razumikhin-type theorem is rst established to obtain the moment stability but with-out almost sure stability. Then an improved edition is presented to derive not only the moment stability but also the almost sure stability, while ex-isting Razumikhin-type theorems aim at only the moment stability. By virtue of the M-matrix techniques, we further develop the aforementioned Razumikhin-type theorems to be easily implementable. Two examples are given for illustration.
참고문헌 (24)
- J. A. D Appleby, "Decay and growth rates of solutions of scalar stochastic delay differ- ential equations with unbounded delay and state dependent noise", Stoch. Dyn, 5(2), pp.133~147 (2005)
- L. Arnold, "Stochastic Differential Equations: Theory and applications" (1974), Wiley
- A. Berman, "Nonnegative Matrices in the Mathematical Sciences" (1994), SIAM
- J. Cermak, "The asymptotics of solutions for a class of delay differential equations", Rocky Mountain J. Math, 33(3), pp.775~786 (2003)
- J. Cermak, "Asymptotic estimation for some nonlinear delay differential equations", Recults Math, 51(3), pp.201~213 (2008)
- M. L. Heard, "A change of variables for functional differential equations", J. Differential Equations, 18, pp.1~10 (1975)
- D. J. Higham, "Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations", SIAM J. Numer. Anal, 45(2), pp.592~609 (2007)
- A. Iserles, "On the generalized pantograph functional-differential equation", European J. Appl. Math, 4(1), pp.1~38 (1993)
- R. Z. Khas'minskii, "Stochastic Stability of Differential Equations", Sijthoff and Noordhoff, ~ (1981)
- V. B. Kolmanovskii, "Stability of Functional Differential Equations" (1986), Academic Press
- G. Makay, "On the asymptotic behavior of the pantograph equations", Elec- tron. J. Qual. Theory Differ. Equ, 1998(2), pp.1~12 (1998)
- X. Mao, "Exponential Stability of Stochastic Differential Equations" (1994), Dekker
- X. Mao, "Razumikhin-type theorems on exponential stability of stochastic functional dif- ferential equations, Stochastic Process", Stochastic Process. Appl, 65(2), pp.233~250 (1996)
- X. Mao, "Razumikhin-type theorems on exponential stability of neutral stochastic func- tional differential equations", SIAM J. Math. Anal, 28(2), pp.389~401 (1997)
- X. Mao, "Stochastic Differential Equations and Applications" (1997), Horwood
- X. Mao, "A note on the LaSalle-type theorems for stochastic differential delay equations", J. Math. Anal. Appl, 268(1), pp.125~142 (2002)
- X. Mao, "LaSalle-type theorems for stochastic differential delay equations", J. Math. Anal. Appl, 236(2), pp.350~369 (1999)
- X. Mao, "The LaSalle-type theorems for stochastic functional differential equations", Non- linear Stud, 7(2), pp.307~328 (2000)
- 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(6), pp.1551~1566 (2007)
- X. Mao, "Stochastic differential delay equations with Markovian switching", Bernoulli, 6(1), pp.73~90 (2000)
- X. Mao, "Khasminskii-type theorems for stochastic differential delay equations", Stoch. Anal. Appl, 23(5), pp.1045~1069 (2005)
- X. Mao, "Stochastic Differential Equations with Markovian Switching" (2006), Im- perial College press
