| Elshan Ibayev Investigation of the Boundary Functional of the Random Walk Process with a Special Barrier |
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| Abstract. In this paper we consider a complex stochastic process that incorporates random walk behavior with variable durations in each state, including negative drift and positive jumps. We derive an integral equation for the Laplace transform of the conditional distribution of the boundary functional. In this work, we define the residence time of a system using a mathematical model based on absolutely continuous distribution with varying parameters. Each parameter could represent a different characteristic of the system. The main objective of the paper is to reduce the integral equation for the Laplace transform to a fractional order differential equation with constant coefficients. |
| Keywords: Inverse Laplace transform, semi-Markov process, Riemann-Liouville fractional derivative |
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