Mathematical Notes

, Volume 104, Issue 5–6, pp 623–627 | Cite as

On the Distribution of the First Component ηt of a Controlled Poisson Process {ηt, ξt}, t ≥ 0, without Boundary

  • T. M. AlievEmail author
  • K. K. Omarova


An ergodicity condition for the first component ηt of a controlled Poisson process without boundary is found. The Laplace transform of the same component ηt, t ≥ 0, is obtained from the given transition probabilities of the process {ηt, ξt}, t ≥ 0. It is essential that the given process {ηt, ξt}, t ≥ 0, is a Markov process homogeneous in the second component.


Poisson process ergodicity condition homogeneous Markov process Laplace transform 


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© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Institute of Control SystemsNational Academy of Sciences of AzerbaijanBakuAzerbaijan

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