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Approximate formulas for stationary characteristics of a renewal-reward process in a strip

Khaniyev Tahir et al · De Gruyter · 2026

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Author / responsible party
Khaniyev Tahir et al
Publisher
De Gruyter
Year
2026
ISSN
2391-4661
ISSN
2391-4661
Language
English

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This study examines a modification of a renewal-reward process in a strip. First, the study proves that this process is ergodic under certain conditions. Then, the exact formulas are obtained for the ergodic distribution and moments of the process in the subject. Moreover, using the asymptotic properties of the Error function and the Laplace transform, we derive two-term asymptotic expansions for the ergodic distribution and its moments. Finally, using these expansions, the study proves that the ergodic distribution of the standardized process weakly converges to a uniform distribution.

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APA 7

al, K. T. E. (2026). Approximate formulas for stationary characteristics of a renewal-reward process in a strip. https://doi.org/10.1515/dema-2025-0230

MLA

al, Khaniyev Tahir et. "Approximate formulas for stationary characteristics of a renewal-reward process in a strip." 2026. https://doi.org/10.1515/dema-2025-0230.

Chicago

al, Khaniyev Tahir et. 2026. "Approximate formulas for stationary characteristics of a renewal-reward process in a strip.". https://doi.org/10.1515/dema-2025-0230.

Harvard

al, K. T. E. 2026, Approximate formulas for stationary characteristics of a renewal-reward process in a strip, De Gruyter, available at: https://doi.org/10.1515/dema-2025-0230 [Accessed 7 Aug. 2026].

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Title
Approximate formulas for stationary characteristics of a renewal-reward process in a strip
Author / contributors
Khaniyev Tahir et al
Publisher
De Gruyter
Publication year
2026
ISSN
2391-4661
ISSN
2391-4661
Language
English

Subjects

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renewal-reward process in a strip; ergodic distribution; weak convergence; approximated formulas; error function; 60k15; 60k05
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