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We study the instabilities of a harmonic oscillator subject to additive anddichotomous multiplicative noise, focussing on the dependance of theinstability threshold on the mass. For multiplicative noise in the damping, theinstability threshold is crossed as the mass is decreased, as long as thesmaller damping is in fact negative. For multiplicative noise in the stiffness,the situation is more complicated and in fact the transition is reentrant forintermediate noise strength and damping. For multiplicative noise in the mass,the results depend on the implementation of the noise. One can take thevelocity or the momentum to be conserved as the mass is changed. In these casesincreasing the mass destabilizes the system. Alternatively, if the change inmass is caused by the accretion/loss of particles to the Brownian particle,these processes are asymmetric with momentum conserved upon accretion andvelocity upon loss. In this case, there is no instability, as opposed to theother two implementations. We also study the distribution of the energy,finding a power-law cutoff at a value which increases with time.

Mass Dependence of Instabilities of an Oscillator with Multiplicative and Additive Noise