On the Boundary Functional of a Semi-Markov Process

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Fundamentals of Contemporary Mathematical Sciences
Volume:5 Issue:2
On the Boundary Functional of a Semi-Markov Process

On the Boundary Functional of a Semi-Markov Process

Authors : Elshan Ibayev

Pages : 123-133

Doi:10.54974/fcmathsci.1387316

View : 37 | Download : 34

Publication Date : 2024-07-31

Article Type : Research Paper

Abstract :In this paper, we consider the semi-Markov random walk process with negative drift, positive jumps. An integral equation for the Laplace transform of the conditional distribution of the boundary functional is obtained. In this work, we define the residence time of the system by generalized exponential distributions with different parameters via fractional order integral equation. The purpose of this paper is to reduce an integral equation for the Laplace transform of the conditional distribution of a boundary functional of the semi-Markov random walk processes to fractional order differential equation with constant coefficients.
Keywords : Laplace transform, random variable, semi Markov random walk process, Riemann Liouville fractional derivative

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