Lyapunov exponents of nilpotent ito systems

References

• Arnold , L. , Oeljeklaus , E. and Paradoux , E. 1985 . “ Almost sure and moment stability for linear Ito equations, in ” . In Lyapunov exponents , Edited by: Arnold , L. and Wihstutz , V. Vol. 1186 , 129 – 159 . Springer Verlag . Lecture Notes in Mathematics
   Google Scholar
• Ichihara , K. and Kunita , H. 1974,1977 . A classification of the second-order degenerate ellptic operators and its probabilistic characterization, Z . Wahrscheinlichkeitstheorie , 30,39 : 235,81 – 254,84 .
   Google Scholar
• Auslender , E. I. and Mil'shtein , G.N. 1983 . Asymptotic expansion of the Lyapunov index for linear stochastic systems with small noise . Prikl Math. Mekh., USSR , 46 : 277 – 283 .
   Web of Science ®Google Scholar
• Arnold , L. , Papanicolaou , G.C. 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 .
   Web of Science ®Google Scholar
• von Karman , Th. and Biot , Maurice A. 1940 . Mathematical Methods in Engineering , 267 New York : McGraw Hill .
   Google Scholar
• Paradoux , E. and Wihstutz , V. 1988 . Lyapunov exponent and rotation number of two-dimensional stochastic systems with small diffusion . SIAM Journal of Applied Math , 48 : 442 – 457 .
   Google Scholar
• Paradoux , E. and Wihstutz , V. Lyapunov exponent of linear stochastic systems with large diffusion term , preprint .
   Google Scholar
• Sussmann , H. and Jurdjevic , V. 1972 . Controllability of non-linear systems . Journal of Differential Equations , 12 : 95 – 116 .
   Web of Science ®Google Scholar