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

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Abstract

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.

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Correspondence to T. M. Aliev.

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Original Russian Text © T. M. Aliev, K. K. Omarova, 2018, published in Matematicheskie Zametki, 2018, Vol. 104, No. 5, pp. 643–648.

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Aliev, T.M., Omarova, K.K. On the Distribution of the First Component ηt of a Controlled Poisson Process {ηt, ξt}, t ≥ 0, without Boundary. Math Notes 104, 623–627 (2018). https://doi.org/10.1134/S0001434618110019

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  • DOI: https://doi.org/10.1134/S0001434618110019

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