Effet d'un bruit blanc sur l'oscillateur harmonique de dimension d

Nathanaël Enriquez

Annales de l'I.H.P. Probabilités et statistiques (1996)

  • Volume: 32, Issue: 5, page 601-622
  • ISSN: 0246-0203

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Enriquez, Nathanaël. "Effet d'un bruit blanc sur l'oscillateur harmonique de dimension d." Annales de l'I.H.P. Probabilités et statistiques 32.5 (1996): 601-622. <http://eudml.org/doc/77548>.

@article{Enriquez1996,
author = {Enriquez, Nathanaël},
journal = {Annales de l'I.H.P. Probabilités et statistiques},
keywords = {isotropic harmonic oscillator; Lyapunov exponent; perturbation method},
language = {fre},
number = {5},
pages = {601-622},
publisher = {Gauthier-Villars},
title = {Effet d'un bruit blanc sur l'oscillateur harmonique de dimension d},
url = {http://eudml.org/doc/77548},
volume = {32},
year = {1996},
}

TY - JOUR
AU - Enriquez, Nathanaël
TI - Effet d'un bruit blanc sur l'oscillateur harmonique de dimension d
JO - Annales de l'I.H.P. Probabilités et statistiques
PY - 1996
PB - Gauthier-Villars
VL - 32
IS - 5
SP - 601
EP - 622
LA - fre
KW - isotropic harmonic oscillator; Lyapunov exponent; perturbation method
UR - http://eudml.org/doc/77548
ER -

References

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  1. [1] L. Arnold, G. Papanicolaou and V. Wihstutz, Asymptotic analysis of the Lyapunov exponent and rotation number of the random oscillator and applications, SIAM Journal Appl. Math., Vol. 46, 1986, p. 427-449. Zbl0603.60051MR841459
  2. [2] E.I. Auslender and G.N. Mil'shtein, Lyapunov expansions of the Lyapunov index for linear stochastic systems with small noise, Prikl. Math. Mekh., Vol. 46, 1982, p. 358-365. En Russe. J. Appl. Math. Mech., 1983, p. 277-283. En Anglais. Zbl0522.34053MR709667
  3. [3] N. Enriquez, Effet d'un bruit blanc sur l'oscillateur harmonique de dimension d, Note au CRAS, 1994. Zbl0794.60057
  4. [4] G.B. Gurevitch, Foundations of the theory of algebraic invariants, Groningen: Noordhoff, 1964. Zbl0128.24601MR183733
  5. [5] Y. Le Jan, On isotropic brownian motion, ZfW, Vol. 70, 1985, p. 609-620. Zbl0576.60072MR807340
  6. [6] W. Magnus, F. Oberhettinger and R.P. Soni, Formulas and theorems for the special functions of mathematical physics, Springer-Verlag, New-York Inc., 1966, Chap 2. Zbl0143.08502MR232968
  7. [7] Oseledec, A multiplicative ergodic theorem. Lyapunov characteristic numbers for dynamical system, Trans. Moscow Math. Soc., Vol. 19, 1968, p. 197-230. Zbl0236.93034
  8. [8] E. Pardoux and V. Wihstutz, Lyapunov exponent and rotationnumber of two-dimensional linear stochastic systems with small diffusion noise, SIAM Journal Appl. Math., Vol. 48, 1988, p. 442-457. Zbl0641.60065MR933045
  9. [9] M. Pinsky, Extremal character of the Lyapunov exponent of the stochastic harmonic oscillator, Annals of Appl. Prob., Vol. 2, 1992, p. 942-950. Zbl0788.60072MR1189424
  10. [10] M. Pinsky and V. Wihstutz, Lyapunov exponents of nilpotent Itô systems, Stochastics, Vol. 25, 1988, p. 43-57. Zbl0654.60043MR1008234

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