Journal of Statistical Physics

, Volume 9, Issue 1, pp 45–50 | Cite as

Generalized master equations for continuous-time random walks

  • V. M. Kenkre
  • E. W. Montroll
  • M. F. Shlesinger


An equivalence is established between generalized master equations and continuous-time random walks by means of an explicit relationship betweenψ(t), which is the pausing time distribution in the theory of continuous-time random walks, andφ(t), which represents the memory in the kernel of a generalized master equation. The result of Bedeaux, Lakatos-Lindenburg, and Shuler concerning the equivalence of the Markovian master equation and a continuous-time random walk with an exponential distribution forψ(t) is recovered immediately. Some explicit examples ofφ(t) andψ(t) are also presented, including one which leads to the equation of telegraphy.

Key words

Generalized master equations random walks statistical mechanics transport theory 


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Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

  • V. M. Kenkre
    • 1
  • E. W. Montroll
    • 1
  • M. F. Shlesinger
    • 1
  1. 1.Institute for Fundamental Studies, Department of Physics and AstronomyUniversity of RochesterRochester

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