Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Toward a theory of random semi-Markov processes


Matrix differences and integral equations are introduced for the description of finite-valued non markovian random processes. In a special case we deduce an integral equation of a semi-Markov process. Necessary conditions are found for a semi-Markov process to be markovian. A generalized understanding of a semi-Markov random process is offered.

This is a preview of subscription content, log in to check access.

Literature cited

  1. 1.

    S. M. Brodi and N. A. Pogosyan, Stochastic Processes in Queueing Theory [in Russian], Kiev (1973).

  2. 2.

    A. N. Kolmogorov, “On analytic methods of probability theory,” Usp. Mat. Nauk,5, 5–41 (1938).

  3. 3.

    V. S. Korlyuk and A. F. Turbin, Mathematical Foundations of Phase Amplification in Complex Systems [in Russian], Kiev (1978).

  4. 4.

    V. I. Tikhonov and V. A. Markov, Markov Processes [in Russian], Moscow (1977).

Download references

Author information

Additional information

Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 121–128, 1989.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Valeev, K.G., Sulima, J.M. Toward a theory of random semi-Markov processes. J Math Sci 67, 3131–3136 (1993).

Download citation


  • Integral Equation
  • Random Process
  • Generalize Understanding
  • Matrix Difference
  • Markovian Random Process