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Effect of a white noise on the $$d$$-dimensional harmonic oscillator. (Effet d’un bruit blanc sur l’oscillateur harmonique de dimension $$d$$.) (French) Zbl 0794.60057
Summary: We compute by a perturbative method an equivalent of the almost sure Lyapunov exponent of the random isotropic harmonic oscillator in the case of small perturbations.
##### MSC:
 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)