Harmonic oscillator with fluctuating mass

We generalize the previously considered cases of a harmonic oscillator subject to a random force (Brownian motion), or having random frequency, or random damping. We consider here a random mass which corresponds to an oscillator where the particles of the surrounding medium adhere to the oscillator for some (random) time after collision, thereby changing the oscillator mass. Such a model is appropriate to chemical and biological solutions as well as to some nano-technological devices. The first moment and stability conditions for white and dichotomous noise are analyzed.