Communication cascade processes with Markov chains

  • T. A. Shmygaleva
  • E. V. Shmygalev
  • A. I. Kupchishin
  • L. Sh. Cherykbaeva
  • Zh. E. Temirbekova


The work executed within the framework of cascade-probability method, the essence of which is to obtain and further use of cascade-probability functions (CPF) for the different particles. CPF sense the probability that a particle generated at a certain depth h’ reaches a certain depth h after the n-th number of collisions. We have considered the interaction of ions with solids and communication processes of radiation defect with Markov processes and Markov chains. Displaying obtain recurrence relations for the simplest of CPF Chapman-Kolmogorov equations. In this case the particle after the collision does not change its direction of movement, the flow rate is independent of time, and hence the penetration depth. recurrence relations are also obtained for the RAF taking into account losses of energy to the ions of the Chapman-Kolmogorov equation, the intensity of the flow depends on the depth of penetration.


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How to Cite
SHMYGALEVA, T. A. et al. Communication cascade processes with Markov chains. International Journal of Mathematics and Physics, [S.l.], v. 7, n. 1, p. 10-15, june 2016. ISSN 2409-5508. Available at: <>. Date accessed: 19 june 2018. doi:


cascade-probability, ions, defect formation, Markov chain, Markov processes.