Asymptotic Derivation of Langevin-like Equation with Non-Gaussian Noise and Its Analytical Solution

Kiyoshi Kanazawa, Tomohiko G. Sano, Takahiro Sagawa, Hisao Hayakawa

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


We asymptotically derive a non-linear Langevin-like equation with non-Gaussian white noise for a wide class of stochastic systems associated with multiple stochastic environments, by developing the expansion method in our previous paper (Kanazawa et al. in Phys Rev Lett 114:090601–090606, 2015). We further obtain a full-order asymptotic formula of the steady distribution function in terms of a large friction coefficient for a non-Gaussian Langevin equation with an arbitrary non-linear frictional force. The first-order truncation of our formula leads to the independent-kick model and the higher-order correction terms directly correspond to the multiple-kicks effect during relaxation. We introduce a diagrammatic representation to illustrate the physical meaning of the high-order correction terms. As a demonstration, we apply our formula to a granular motor under Coulombic friction and get good agreement with our numerical simulations.

Original languageEnglish
Pages (from-to)1294-1335
Number of pages42
JournalJournal of Statistical Physics
Issue number5
Publication statusPublished - 2015 Sept 1
Externally publishedYes


  • Granular motor
  • Langevin equation
  • Non-Gaussian noise
  • Non-linear friction
  • Stochastic processes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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