https://cea.hal.science/cea-02927301Mallick, KironeKironeMallickIPHT - Institut de Physique Théorique - UMR CNRS 3681 - CEA - Commissariat à l'énergie atomique et aux énergies alternatives - Université Paris-Saclay - CNRS - Centre National de la Recherche ScientifiqueRandom oscillator with general Gaussian noiseHAL CCSD2007Langevin dynamicsMultiplicative noiseNonlinear oscillations[PHYS.COND.CM-SM] Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech]Savelli, Bruno2020-09-01 15:28:082023-03-24 14:53:182020-09-01 15:37:02enJournal articleshttps://cea.hal.science/cea-02927301/document10.1016/j.physa.2007.04.070application/pdf1We study the long time behaviour of a nonlinear oscillator subject to a random multiplicative noise with a spectral density (or power-spectrum) that decays as a power law at high frequencies. When the dissipation is negligible, physical observables, such as the amplitude, the velocity and the energy of the oscillator grow as power-laws with time. We calculate the associated scaling exponents and we show that their values depend on the asymptotic behaviour of the external potential and on the high frequencies of the noise. Our results are generalized to include dissipative effects and additive noise.