Journal of Statistical Physics

, Volume 29, Issue 4, pp 773–779 | Cite as

Asymptotic results on occupancy times of random walks

  • K. P. N. Murthy
  • M. C. Valsakumar


In this note we derive, using Wald's theorem asymptotic results on mean occupancy time of an interval for random walks with arbitrary transition probabilities. We show that our results are consistent with those obtained (by Weiss, Ref. 2) via the master equation approach, by demonstrating that the resulting infinite series can be summed exactly.

Key words

Lattice random walks occupation times first passage times continuum limit Wald's identity 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    D. Gutkowicz-Krusin, I. Proccaecia, and J. Ross,J. Stat. Phys. 19:525 (1978).Google Scholar
  2. 2.
    G. H. Weiss,J. Stat. Phys. 21:609 (1979).Google Scholar
  3. 3.
    A. Wald,Sequential Analysis (Wiley, New York, 1947).Google Scholar
  4. 4.
    William A. Feller,An Introduction to Probability Theory and its Applications (Wiley Eastern, New Delhi, 1977).Google Scholar

Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • K. P. N. Murthy
    • 1
  • M. C. Valsakumar
    • 2
  1. 1.Fast Reactor GroupReactor Research CentreTamil NaduIndia
  2. 2.Materials Science LaboratoryReactor Research CentreTamil NaduIndia

Personalised recommendations