On the Rate of Convergence for a Characteristic of Multidimensional Birth-Death Process

Alexander Zeifman, Yacov Satin, Ksenia Kiseleva and Victor Korolev
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Alexander Zeifman: Department of Applied Mathematics, Vologda State University, IPI FRC CSC RAS, VolSC RAS, 160000 Vologda, Russia
Yacov Satin: Department of Mathematics, Vologda State University, 160000 Vologda, Russia
Ksenia Kiseleva: Department of Applied Mathematics, Vologda State University, 160000 Vologda, Russia
Victor Korolev: Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow, Russia

Mathematics, 2019, vol. 7, issue 5, 1-10

Abstract: We consider a multidimensional inhomogeneous birth-death process. In this paper, a general situation is studied in which the intensity of birth and death for each coordinate (“each type of particle”) depends on the state vector of the whole process. A one-dimensional projection of this process on one of the coordinate axes is considered. In this case, a non-Markov process is obtained, in which the transitions to neighboring states are possible in small periods of time. For this one-dimensional process, by modifying the method previously developed by the authors of the note, estimates of the rate of convergence in weakly ergodic and null-ergodic cases are obtained. The simplest example of a two-dimensional process of this type is considered.

Keywords: multidimensional birth-death process; inhomogeneous continuous-time Markov chain; rate of convergence; one dimensional projection (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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