Birth–Death Processes with Two-Type Catastrophes

Abstract

This paper concentrates on the general birth–death processes with two different types of catastrophes. The Laplace transform of transition probability function for birth–death processes with two-type catastrophes is successfully expressed with the Laplace transform of transition probability function of the birth–death processes without catastrophe. The first effective catastrophe occurrence time is considered. The Laplace transform of its probability density function, expectation and variance are obtained.

Keywords

• birth–death process
• catastrophe
• Laplace transform
• probability density function