Abstract
The aim of this paper is to summarize both theoritical and numerical results concerning the dependence of the Lyapunov exponent of the solution of the solution of a linear equation, in terms of some parameters describing the law of the parametric excitation.
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References
L.ARNOLD: Stochastic Differential Equations, J.Wiley (1974)
L.ARNOLD, W.KLIEMANN, & E.OELJEKLAUS: Lyapunov Exponent of a linear stochastic system, Lyapunov Exponents, L.Arnold & V.Wihstutz Ed., Lecture Notes in Mathematics 1186, Springer, 1986.
L.ARNOLD, E.OELJEKLAUS & E.PARDOUX: Almost sure and moment stability for linear Ito Equations, Lyapunov Exponents, L.Arnold & V.Wihstutz Ed., Lecture Notes in Mathematics 1186, Springer, 1986.
L.ARNOLD, G.PAPANICOLAOU & V.WIHSTUTZ: Asymptotic analysis of the Lyapunov exponent and rotation number of the random oscillator and applications, Siam J. Applied Math. 46 (1986), 427–450.
E.I. AUSLENDER G.N.MIL’SHTEIN: Asymptotic expansion of the Lyapunov index for linear stochastic systems with small noise, Prikl. Matem. Mekhan. 46, 3 (1982), 358–365.
R.N. BHATTACHARYA: On the functional central limit theorem and the law of the iterared logarithm for Markov processes, Z. Wahrscheinlichkeitstheorie verw. Gebiete 60 (1982), 185–201.
R.BOUC & E.PARDOUX: Asymptotic analysis of PDEs with wide-band noise disturbances, and expansion of the moments, Stoch. Anal. and Appl. 2 (1984), 369–422.
P.BOUGEROL: Théorèmes limites pour les systèmes linéaires à coefficients markoviens (to appear); see also: P.BOUGEROL & J.LACROIX: Products of random matrices with applications to Schrodinger operators, Birkhauser (1985)
Y.LIN & S.ARIARATNAM: Stability of bridge motion in turbulent winds, J. Struct. Mech. 8 (1980), 1–15
E. PARDOUX: Wide band limit of Lyapunov-exponents, Stochastic Differential Systems, N.Christopeit, K.Helmes, M.Kohlmann Ed., Lecture Notes in Control and Information Sciences 78, Springer-Verlag (1986)
E. PARDOUX: Stabilité du mouvement des pales d’hélicoptères dans le cas d’un écoulement de l’air turbulent, Actes du Colloque “L’Automatique pour l’Aéronautique”, Paris (1986)
E. PARDOUX & D.TALAY: Discretization and simulation of S.D.E., Acta Applicandae Mathematicae 3, 23, 1985.
E. PARDOUX & V.WIHSTUTZ: Lyapunov exponent and rotation number of two-dimensional linear stochastic systems with small diffusion term, Siam J. Applied Math., to appear.
E. PARDOUX & V.WIHSTUTZ: Lyapunov exponent of linear stochastic systems with large diffusion term, to appear.
M.PINSKY: Instability of the harmonic oscillator with small noise, Siam J.Applied Math. 46 (1986), 451–463
M.PIGNOL: Stabilité stochastique des pales d'hélicoptère, Thèse de 3ème Cycle, Université de Provence (1985)
M.PINSKY & V.WIHSTUTZ: in preparation
J.PRUSSING & Y.LIN: Rotor blade flap-lag stability in turbulent flows, J. of the Amer. Helicopter Soc. (1982), 51–57
D.TALAY: Classification of discretization schemes of diffusions according to an ergodic criterium, Stochastic Modelling and Filtering, A.Germani Ed., Lecture Notes in Control & Information Sciences 91 (1987)
D.TALAY: Calcul numérique des exposants de Lyapounov, Rapport INRIA, to appear.
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© 1988 Springer-Verlag Berlin Heidelberg
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Pardoux, E., Talay, D. (1988). Stability of Linear Differential Systems with Parametric Excitation. In: Ziegler, F., Schuëller, G.I. (eds) Nonlinear Stochastic Dynamic Engineering Systems. IUTAM Symposium. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83334-2_11
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DOI: https://doi.org/10.1007/978-3-642-83334-2_11
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