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 - 2003 |
All Science Journal Classification (ASJC) codes
- Statistics and Probability
- Statistics, Probability and Uncertainty
- Management Science and Operations Research
- Industrial and Manufacturing Engineering