Mean-square displacement of a stochastic oscillator: Linear vs quadratic noise

► We consider the Brownian motion for a harmonically bound particle with adhesion. ► The adhesion means that the mass of the Brownian particle becomes a random variable. ► For white-noise randomness of the mass, the second moment is the same as for usual Brownian motion. ► For dichotomous-noise randomness, the second moment may show the “energetic” instability. ► For all types of multiplicative noise, replacement of linear noise by quadratic one leads to the increase of stability.