On non-time-homogeneity

  • Hermann Thorisson


The assumption of time-homogeneity is implicit in many stochastic models. This is considered necessary for some calculations and limit results. However, in many applications the time-homogeneity condition is far from realistic. Here we propose two ways of attacking the problem of non-time-homogeneity.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. D. Blackwell (1945), Finite non-homogeneous chains. Ann. Math. 46, 594–599.MathSciNetzbMATHCrossRefGoogle Scholar
  2. E. Çinlar (1975), Introduction to Stochastic Processes. Prentice-Hall Inc. Englewood Cliffs, New Jersey.zbMATHGoogle Scholar
  3. H. Cohn (1974), On the tail events of a Markov chain. Z. Wahrscheinlichkeitsth. 29, 65–72.zbMATHCrossRefGoogle Scholar
  4. H. Cohn (1982), On a class of non-homogeneous Markov chains. Math. Proc. Comb. Phil. Soc. 92, 527–534.zbMATHCrossRefGoogle Scholar
  5. D. Griffeath (1978), Coupling methods for Markov processes. Studies in Probability and Ergodic Theory. Adv. Math. Supplementary Studies 2.Google Scholar
  6. A.N. Kolmogorov (1936), Zur Theorie der Markoffschen Ketten. Math. Ann. 112, 155–160.MathSciNetCrossRefGoogle Scholar
  7. H. Thorisson (1983), The coupling of regenerative processes. Adv. Appl. Prob. 15, 531–561.MathSciNetzbMATHCrossRefGoogle Scholar
  8. H. Thorisson (1985), The queue GI/GI/k: Finite moments of the cycle variables and uniform rates convergence. Stochastic Models, 1(2), 221–238.MathSciNetzbMATHCrossRefGoogle Scholar
  9. H. Thorisson, On regenerative and ergodic properties of the k-server queue with non-stationary Poisson arrivals. To appear in J. Appl. Prob.Google Scholar
  10. H. Thorisson (1984), Backward limits of non-time-homogeneous regenerative processes. Preprint, Dept. Math. Göteborg.Google Scholar
  11. H. Thorisson, On maximal and distributional coupling. To appear in Annals of Probability.Google Scholar

Copyright information

© Springer Science+Business Media New York 1986

Authors and Affiliations

  • Hermann Thorisson
    • 1
  1. 1.Department of MathematicsChalmers University of Technology and the University of GöteborgGöteborgSweden

Personalised recommendations