Abstract
Very few stochastic systems are known to have closed-form transient solutions. In this article we consider an immigration birth and death population process with total catastrophes and study its transient as well as equilibrium behavior. We obtain closed-form solutions for the equilibrium distribution as well as the closed-form transient probability distribution at any time t ≥ 0. Our approach involves solving ordinary and partial differential equations, and the method of characteristics is used in solving partial differential equations.
| Original language | English (US) |
|---|---|
| Pages (from-to) | 83-106 |
| Number of pages | 24 |
| Journal | Probability in the Engineering and Informational Sciences |
| Volume | 17 |
| Issue number | 1 |
| DOIs | |
| State | Published - Jan 1 2003 |
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All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
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Transient analysis of immigration birth-death processes with total catastrophes. / Chao, Xiuli; Zheng, Yuxi.
In: Probability in the Engineering and Informational Sciences, Vol. 17, No. 1, 01.01.2003, p. 83-106.Research output: Contribution to journal › Article
TY - JOUR
T1 - Transient analysis of immigration birth-death processes with total catastrophes
AU - Chao, Xiuli
AU - Zheng, Yuxi
PY - 2003/1/1
Y1 - 2003/1/1
N2 - Very few stochastic systems are known to have closed-form transient solutions. In this article we consider an immigration birth and death population process with total catastrophes and study its transient as well as equilibrium behavior. We obtain closed-form solutions for the equilibrium distribution as well as the closed-form transient probability distribution at any time t ≥ 0. Our approach involves solving ordinary and partial differential equations, and the method of characteristics is used in solving partial differential equations.
AB - Very few stochastic systems are known to have closed-form transient solutions. In this article we consider an immigration birth and death population process with total catastrophes and study its transient as well as equilibrium behavior. We obtain closed-form solutions for the equilibrium distribution as well as the closed-form transient probability distribution at any time t ≥ 0. Our approach involves solving ordinary and partial differential equations, and the method of characteristics is used in solving partial differential equations.
UR - http://www.scopus.com/inward/record.url?scp=0037252769&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=0037252769&partnerID=8YFLogxK
U2 - 10.1017/S0269964803171057
DO - 10.1017/S0269964803171057
M3 - Article
AN - SCOPUS:0037252769
VL - 17
SP - 83
EP - 106
JO - Probability in the Engineering and Informational Sciences
JF - Probability in the Engineering and Informational Sciences
SN - 0269-9648
IS - 1
ER -