A diffusion model for a system subject to random shocks
- Authors
- Lee, Eui Yong; Song, Mun-Sup; Park, Byung-Gu
- Issue Date
- Jun-1995
- Publisher
- The Korean Statistical Society
- Keywords
- Diffusion model; Random shocks; Poisson process; First passage time
- Citation
- Journal of the Korean Statistical Society, v.24, no.1, pp 141 - 147
- Pages
- 7
- Journal Title
- Journal of the Korean Statistical Society
- Volume
- 24
- Number
- 1
- Start Page
- 141
- End Page
- 147
- URI
- https://scholarworks.sookmyung.ac.kr/handle/2020.sw.sookmyung/159371
- ISSN
- 1226-3192
2005-2863
- Abstract
- A diffusion model for a system subject to random shocks is introduced. It is assumed that the state of system is modeled by a Brownian motion with negative drift and an absorbing barrier at the origin. It is also assumed that the shocks coming to the system according to a Poisson process decrease the state of the system by a random amount. It is further assumed that a repairman arrives according to another Poisson process and repairs or replaces the system i the system, when he arrives, is in state zero. A forward differential equation is obtained for the distribution function of X(t), the state of the systme at time t, some boundary conditions are discussed, and several interesting characteristics are derived, such as the first passage time to state zero, F(0,t), the probability of the system being in state zero at time t, and F(0), the limit of F(0,t) as t tends to infinity.
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