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Mat. Zametki, 2017, Volume 102, Issue 4, Pages 490–502 (Mi mz8646)  

On the Limiting Behavior of the Characteristic Function of the Ergodic Distribution of the Semi-Markov Walk with Two Boundaries

R. T. Alievab, T. A. Khanievcb

a Baku State University
b Institute of Control Systems, National Academy of Sciences of Azerbaijan
c TOBB Economy and Technology University, Turkey

Abstract: The semi-Markov walk $(X(t))$ with two boundaries at the levels 0 and $\beta >0$ is considered. The characteristic function of the ergodic distribution of the process $X(t)$ is expressed in terms of the characteristics of the boundary functionals $N(z)$ and $S_{N(z)}$, where $N(z)$ is the first moment of exit of the random walk $\{S_{n}\}$, $n\ge 1$, from the interval $(-z,\beta-z)$, $z\in [0,\beta]$. The limiting behavior of the characteristic function of the ergodic distribution of the process $W_{\beta}(t)=2X(t)/\beta-1$ as $\beta \to \infty$ is studied for the case in which the components of the walk ($\eta_{i}$) have a two-sided exponential distribution.

Keywords: semi-Markov walk, characteristic function of the ergodic distribution of the semi-Markov walk.

DOI: https://doi.org/10.4213/mzm8646

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English version:
Mathematical Notes, 2017, 102:4, 444–454

Bibliographic databases:

Document Type: Article
UDC: 519.21
Received: 07.09.2009
Revised: 09.10.2015

Citation: R. T. Aliev, T. A. Khaniev, “On the Limiting Behavior of the Characteristic Function of the Ergodic Distribution of the Semi-Markov Walk with Two Boundaries”, Mat. Zametki, 102:4 (2017), 490–502; Math. Notes, 102:4 (2017), 444–454

Citation in format AMSBIB
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