Geodesic
On the Distribution of the First Component~$\eta_{t}$ of a Controlled Poisson Process $\{\eta_{t},\xi_{t}\}$, $t\ge 0$, without Boundary
Matematičeskie zametki, Tome 104 (2018) no. 5, pp. 643-648

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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.
Mots-clés : Poisson process, Laplace transform.
Keywords: ergodicity condition, homogeneous Markov process 
@article{MZM_2018_104_5_a0,
     author = {T. M. Aliyev and K. K. Omarova},
     title = {On the {Distribution} of the {First} {Component~}$\eta_{t}$ of a {Controlled} {Poisson} {Process} $\{\eta_{t},\xi_{t}\}$, $t\ge 0$, without {Boundary}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {643--648},
     publisher = {mathdoc},
     volume = {104},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_104_5_a0/}
}
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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. Matematičeskie zametki, Tome 104 (2018) no. 5, pp. 643-648. http://geodesic.mathdoc.fr/item/MZM_2018_104_5_a0/