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Original Articles

Lyapunov exponent and rotation number of a two-dimensional nilpotent stochastic system

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Pages 1-9 | Published online: 21 Mar 2007

References

  • Arnold , L. , Papanicolaou , G. and Wihstutz , V. 1986 . Asymptotic analysis of the Lyapunov exponent and rotation number of the random oscillator and applications . SIAM Journal of Applied Mathematics , 46 : 427 – 450 .
  • Auslender , E. I. and Mil'shtein , G. N. 1983 . Asymptotic expansions of the Lyapunov index for linear stochastic systems with small noise . Journal of Applied Mathematics and Mechanics (PMM) , 46 : 277 – 283 . English translation
  • Khas'minskii , R. Z. 1967 . Necessary and sufficient conditions for the asymptotic stability of linear stochastic systems . Theory of Probility and Its Applications , 12 : 144 – 147 . (English translation)
  • Kozin , F. and Prodromou , S. 1971 . Necessary and sufficient conditions for almost sure sample stability of linear Itô equations . SIAM Journal of Applied Mathematics , 21 : 413 – 424 .
  • Nishioka , K. 1976 . On the stability of two-dimensional linear stochastic systems . Kodai Mathematics Seminar Reports , 27 : 211 – 230 .
  • Pardoux , E. and Wihstutz , V. 1988 . Lyapunov exponent and rotation number of two-dimensional linear stochastic systems with small diffusion . SIAM Journal of Applied Mathematics , 48 : 442 – 457 .
  • Pinsky , M. A. and Wihstutz , V. 1988 . Lyapunov exponents of nilpotent ltô systems . Stochastics , 25 : 43 – 57 .
  • Prudnikov , A. P. , Brychkov , Yu. A. and Marichev , O. I. 1986 . Integrals and Series (Special Functions) , Vol. 2 , New York : Gordon and Breach . English translation

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