International Journal of Applied Mathematics, Computational Science and Systems Engineering
E-ISSN: 2766-9823
Volume 8, 2026
Researching of Various Realizations of The Semi-Markov Random Process with Positive Tendency and Negative Jump
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Abstract: In recent years, semi-Markov random walks have been employed to address numerous intriguing problems across fields such as inventory management, risk management, insurance, and reliability theories. Particularly, many significant problems in stock control, queue management, and reliability theory can be represented using random walks constrained by two barriers. These barriers, depending on the specific problem, may be reflecting, delaying, absorbing, elastic, or of other types. A key problem in stochastic process theory is determining the Laplace transforms for the distribution of semi-Markov random processes. In this context, this article explores semi-Markov random processes characterized by a positive tendency and negative jumps.
Keywords:
Laplace transforms, semi-Markov random process, random variable, process with positive tendency and negative jumps
Pages: 141-146
DOI: 10.37394/232026.2026.8.14