Stability in distribution of stochastic differential delay equations with Markovian switching

Systems and Control Letters

Volumn 50, Issue 3, 2003, Pages 195-207

  Yuan, Chenggui ^a,b   Zou, Jiezhong ^b   Mao, Xuerong ^a  

^a UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^b CENTRAL SOUTH UNIVERSITY   (China)

Author keywords

Brownian motion; Generalized It 's formula; Markov chain; Stability in distribution

Indexed keywords

BROWNIAN MOVEMENT; DIFFERENTIAL EQUATIONS; MARKOV PROCESSES;

MARKOVIAN SWITCHING;

SYSTEM STABILITY;

EID: 0141569898     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-6911(03)00154-3     Document Type: Article

References (13)

1. Anderson W.J. Continuous-Times Markov Chains. 1991;Springer, Berlin.
2. Basak G.K., Bisi A., Ghosh M.K. Stability of a random diffusion with linear drift. J. Math. Anal. Appl. 202:1996;604-622.
3. Gushchin A.A., Küchler U. On stationary solutions of delay differential equations driven by a Levy process. Stochastic Process. Appl. 88:2000;195-221.
4. Has'minskii R.Z. Stochastic Stability of Differential Equations. 1981;Sijthoff and Noordhoff, Alphen.
5. Ikeda N., Watanable S. Stochastic Differential Equations and Diffusion Processes. 1981;North-Holland, Amsterdam.
6. Ji Y., Chizeck H.J. Controllability, stabilizability and continuous-time Markovian jump linear quadratic control. IEEE Trans. Automat. Control. 35:1990;777-788.
7. Mao X. Exponential Stability of Stochastic Differential Equations. 1994;Marcel Dekker, New York.
8. Mao X. Stochastic Differential Equations and Applications. 1997;Horwood, Chichester.
9. Mao X. Stability of stochastic differential equations with Markovian switching. Stochastic Process. Appl. 79:1999;45-67.
10. Mao X., Matasov A., Piunovskiy A.B. Stochastic differential delay equations with Markovian switching. Bernoulli. 6:2000;73-90.
11. Mariton M. Jump Linear Systems in Automatic Control. 1990;Marcel Dekker, New York.
12. Shaikhet L. Stability of stochastic hereditary systems with Markov switching. Theory Stochastic Process. 2:1996;180-184.
13. Skorohod A.V. Asymptotic Methods in the Theory of Stochastic Differential Equations. 1989;American Mathematical Society, Providence, RI.