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Lyapunov functions and almost sure exponential stability

  • Chapter 2: Nonlinear Random Dynamical Systems
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Lyapunov Exponents

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1486))

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References

  1. Arnold, L., A formula connecting sample and moment stability of linear stochastic systems, SIAM J. Appl. Math. 44 (1984), 793–802.

    Article  MathSciNet  MATH  Google Scholar 

  2. Arnold, L. and Kliemann, W., Qualitative theory of stochastic systems, Probabilistic Analysis and Related Topics, Vol.3 (Bharucha-Reid, A. T., ed.), 1–79, New York, Academic Press 1983.

    Google Scholar 

  3. Arnold, L., Oeljeklaus, E. and Pardoux, E., Almost sure and moment stability for linear Ito equations, Lecture Notes Math. 1186(1984), 129–159.

    Article  MathSciNet  MATH  Google Scholar 

  4. Carverhill, A., Flows of stochastic dynamical systems: ergodic theory, Stochastics 14 (1985), 273–317.

    Article  MathSciNet  MATH  Google Scholar 

  5. Chappell, M., Bounds for average Lyapunov exponents of gradient stochastic systems, Lecture Notes Math. 1186(1984), 292–307.

    MathSciNet  Google Scholar 

  6. Crauel, H., Lyapunov numbers of Markov solutions of linear stochastic systems, Stochastics 14 (1984), 11–28.

    Article  MathSciNet  MATH  Google Scholar 

  7. Curtain, R. (ed.), Stability of stochastic dynamical systems, Lecture Notes Math. 294, Berlin-Heidelberg-New York, Springer 1972.

    MATH  Google Scholar 

  8. Elworthy, K. D., Stochastic Differential Equations on Manifolds, London Math. Society Lecture Note 70, C.U.P, 1982.

    Google Scholar 

  9. Has'minskii, R. Z., Necessary and sufficient conditions for the asymptotic stability of linear stochastic systems, Theory Probability Appl. 12 (1967), 144–147.

    Article  MathSciNet  Google Scholar 

  10. Kunita, H., Stochastic Flows and Stochastic Differential Equations, Cambridge University Press, 1990.

    Google Scholar 

  11. Mao, X., Lebesgue-Stieltjes integral inequality and stochastic stability, Quarterly J. Math. Oxford (2), 40 (1989), 301–311.

    Article  MATH  Google Scholar 

  12. Mao, X., Lyapunov functions and almost sure exponential stability of stochastic differential equations based on semimartingales with spatial parameters, SIAM J. Control and Optimization 28(6) (1990), 1481–1490.

    Article  MathSciNet  MATH  Google Scholar 

  13. Mao, X., Lebesgue-Stieltjes integral inequalities of the Wendroff type in n-independent variables, Chinese J. Math. 17(1) (1989), 29–50.

    MathSciNet  MATH  Google Scholar 

  14. Mao, X. and Wu, R., Existence and uniqueness of the solutions of stochastic differential equations, Stochastics 11 (1983), 19–32.

    Article  MathSciNet  MATH  Google Scholar 

  15. Ladde, G. S., Stochastic stability analysis of model ecosystems with time-delay, in “Differential Equations and Applications in Biology, Epidemics, and Population Problems” edited by S. N. Busenberg and K. Cook, Academic Press (1981), 215–228.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Mathematics Institute, University of Warwick, CV4 7AL, Coventry, England

    Xuerong Mao

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  1. Xuerong Mao
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Ludwig Arnold Hans Crauel Jean-Pierre Eckmann

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© 1991 Springer-Verlag

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Mao, X. (1991). Lyapunov functions and almost sure exponential stability. In: Arnold, L., Crauel, H., Eckmann, JP. (eds) Lyapunov Exponents. Lecture Notes in Mathematics, vol 1486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0086666

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  • DOI: https://doi.org/10.1007/BFb0086666

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54662-7

  • Online ISBN: 978-3-540-46431-0

  • eBook Packages: Springer Book Archive

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