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

M. Gitterman

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Using the Langevin equations, we calculated the stationary second-order moment (mean-square displacement) of a stochastic harmonic oscillator subject to an additive random force (Brownian motion in a parabolic potential) and to different types of multiplicative noise (random frequency or random damping or random mass). The latter case describes Brownian motion with adhesion, where the particles of the surrounding medium may adhere to the oscillator for some random time after the collision. Since the mass of the Brownian particle is positive, one has to use quadratic (positive) noise. For all types of multiplicative noise considered, replacing linear noise by quadratic noise leads to an increase in stability.

Original languageEnglish
Pages (from-to)3033-3042
Number of pages10
JournalPhysica A: Statistical Mechanics and its Applications
Issue number11
StatePublished - 1 Jun 2012


  • Additive and multiplicative linear and quadratic random forces
  • Stationary second moment
  • Stochastic oscillator


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