Abstract
The problem of a harmonic oscillator subject to both additive and multiplicative gaussian noise is solved analytically by means of an iteration procedure. Our solution agrees very closely with earlier predictions available in the literature. The reliability of perturbation approaches to stochastic systems that do not verify the detailed balance conditions is criticized by comparison with exact results worked out for this peculiar model. The effects due to finite correlation times of the fluctuations are also accounted for analytically. All of our predictions have been checked by means of analogue simulation.
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Marchesoni, F., Pochini, M. & Santucci, S. Analogue simulation of stochastic parametric oscillators. Z. Physik B - Condensed Matter 66, 243–248 (1987). https://doi.org/10.1007/BF01311661
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DOI: https://doi.org/10.1007/BF01311661