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Generalized master equations for continuous-time random walks

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Abstract

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.

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Authors and Affiliations

  1. Institute for Fundamental Studies, Department of Physics and Astronomy, University of Rochester, Rochester, New York

    V. M. Kenkre, E. W. Montroll & M. F. Shlesinger

Authors
  1. V. M. Kenkre
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  2. E. W. Montroll
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  3. M. F. Shlesinger
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Additional information

This study was partially supported by ARPA and monitored by ONR Contract No. (N00014-17-C-0308).

For continuity, the reader is directed to the article entitled “Random Walks on Lattices. IV. Continuous Time Walks and Influence of Absorbing Boundaries,” by E. W. Montroll and H. Scher, which will appear in Volume 9, Number 2, of this journal, and which should precede the following article. Regrettably, the two articles were inadvertently switched during processing.

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Kenkre, V.M., Montroll, E.W. & Shlesinger, M.F. Generalized master equations for continuous-time random walks. J Stat Phys 9, 45–50 (1973). https://doi.org/10.1007/BF01016796

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