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Mat. Zametki, 2018, Volume 104, Issue 5, Pages 643–648 (Mi mz11084)  

On the Distribution of the First Component $\eta_{t}$ of a Controlled Poisson Process $\{\eta_{t},\xi_{t}\}$, $t\ge 0$, without Boundary

T. M. Aliyev, K. K. Omarova

Institute of Control Systems, National Academy of Sciences of Azerbaijan

Abstract: An ergodicity condition for the first component $\eta_{t}$ of a controlled Poisson process without boundary is found. The Laplace transform of the same component $\eta_{t}$, $t\ge 0$, is obtained from the given transition probabilities of the process $\{\eta_{t},\xi_{t}\}$, $t\ge 0$. It is essential that the given process $\{\eta_{t},\xi_{t}\}$, $t\ge 0$, is a Markov process homogeneous in the second component.

Keywords: Poisson process, ergodicity condition, homogeneous Markov process, Laplace transform.
Author to whom correspondence should be addressed

DOI: https://doi.org/10.4213/mzm11084

Full text: PDF file (378 kB)
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English version:
Mathematical Notes, 2018, 104:5, 623–627

Bibliographic databases:

UDC: 519.21
Received: 09.12.2015
Revised: 27.12.2017

Citation: T. M. Aliyev, K. K. Omarova, “On the Distribution of the First Component $\eta_{t}$ of a Controlled Poisson Process $\{\eta_{t},\xi_{t}\}$, $t\ge 0$, without Boundary”, Mat. Zametki, 104:5 (2018), 643–648; Math. Notes, 104:5 (2018), 623–627

Citation in format AMSBIB
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\by T.~M.~Aliyev, K.~K.~Omarova
\paper On the Distribution of the First Component~$\eta_{t}$ of a Controlled Poisson Process $\{\eta_{t},\xi_{t}\}$, $t\ge 0$, without Boundary
\jour Mat. Zametki
\yr 2018
\vol 104
\issue 5
\pages 643--648
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\crossref{https://doi.org/10.4213/mzm11084}
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\jour Math. Notes
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\vol 104
\issue 5
\pages 623--627
\crossref{https://doi.org/10.1134/S0001434618110019}
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  • https://doi.org/10.4213/mzm11084
  • http://mi.mathnet.ru/eng/mz/v104/i5/p643

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