Neutral stochastic differential delay equations with Markovian switching

Stochastic Analysis and Applications

Volumn 21, Issue 4, 2003, Pages 819-847

  Kolmanovskii, V ^a   Koroleva, N ^a   Maizenberg, T ^b   Mao, X ^c   Matasov, A ^d  

^a NATIONAL RESEARCH UNIVERSITY HIGHER SCHOOL OF ECONOMICS   (Russian Federation)

^b NATIONAL UNIVERSITY OF SCIENCE AND TECHNOLOGY MISIS   (Russian Federation)

^c UNIVERSITY OF STRATHCLYDE   (United Kingdom)

^d MOSCOW STATE UNIVERSITY   (Russian Federation)

Author keywords

Brownian motion; Generalized It 's formula; Hybrid system; Markov chain

Indexed keywords

EID: 0043074885     PISSN: 07362994     EISSN: None     Source Type: Journal    
DOI: 10.1081/SAP-120022865     Document Type: Article

References (20)

1. Brayton, R. Nonlinear oscillations in a distributed network. Quat. Appl. Math. 1976, 24, 289-301.
2. Rubanik, V.P. Oscillations of Quasilinear Systems with Retardation; Nauka: Moscow, 1969.
3. Hale, J.K.; Lunel, S.M.V. Introduction to Functional Differential Equations; Springer, 1993.
4. Kolmanovskii, V.B.; Nosov, V.R. Stability and Periodic Modes of Control Systems with Aftereffect; Nauka: Moscow, 1981.
5. Mao X. Stochastic Differential Equations and Their Applications; Horwood Pub.: Chichester, 1997.
6. Wilsky, A.S.; Levy, B.C. Stochastic stability research for complex power systems. DOE contract, LIDS, MIT, 1979, Rep. ET-76-C-01-2295.
7. Sworder, D.D.; Rogers, R.O. An LQ-solution to a control problem associated with solar thermal central receiver. IEEE Trans. Automat. Contr. 1983, 28, 971-978.
8. Athans, M. Command and control (C2) theory: A challenge to control science. IEEE Trans. Automat. Contr. 1987, 32, 286-293.
9. Basak, G.K.; Bisi, A.; Ghosh, M.K. Stability of a random diffusion with linear drift. J. Math. Anal. Appl. 1996, 202, 604-622.
10. Ji, Y.; Chizeck, H.J. Controllability, stabilizability and continuous-time Markovian jump linear quadratic control. IEEE Trans. Automat. Control 1990, 35, 777-788.
11. Mao, X. Stability of stochastic differential equations with Markovian switching. Sto. Proc. Their Appl. 1999, 79, 45-67.
12. Mao, X.; Matasov, A.; Piunovskiy, A.B. Stochastic differential delay equations with Markovian switching. Bernoulli 2000, 6(1), 73-90.
13. Mariton, M. Jump Linear Systems in Automatic Control; Marcel Dekker, 1990.
14. Shaikhet, L. Stability of stochastic hereditary systems with Markov switching. Theory of Stochastic Processes 1996, 2 (18) 180-184.
15. Skorohod, A.V. Asymptotic Methods in the Theory of Stochastic Differential Equations; American Mathematical Society: Providence, 1989.
16. Arnold, L. Stochastic Differential Equations: Theory and Applications; John Wiley Sons, 1972.
17. Has'minskii, R.Z. Stochastic Stability of Differential Equations; Sijthoff and Noordhoff, 1981.
18. Ladde, G.S.; Lakshmikantham, V. Random Differential Inequalities; Academic Press, 1980.
19. Mao, X. Exponential Stability of Stochastic Differential Equations; Marcel Dekker, 1994.
20. Mao, X. Stability of Stochastic Differential Equations with Respect to Semimartingales; Longman Scientific and Technical, 1991.