2022, Vol. 7, Issue 6, Part A

A Birth and Death Process is a continuous-time Markov chain that counts the number of particles in a system over time. Each particle can give birth to another particle or die, and the birth and the death rates at any given time depend on the number of existing particles.

The model of the Birth and Death Processes implicate the existence of the famous Chapman Kolmogorov's equation, we have solved this equation according to four homogeneous cases, so in this article we are going to present the solutions found for the resolution of the Chapman Kolmogorov equation in four homogeneous cases, then we add the determination of the parameter γ+,j in a particular case for these four cases. For the same purpose, we will recall the model presented for the homogeneous case and the resolution method followed.