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

Enriquez, Nathanaël

C. R. Acad. Sci., Paris, Sér. I 318, No. 2, 153-155 (1994).

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.)

Keywords:

perturbative method; Lyapunov exponent; random isotropic harmonic oscillator; small perturbations