Maximum likelihood estimation in birth-death process allowing catastrophes

Abstract

The problem of estimating the parameters of the birth - death process al1owing catastrophes or mass emigration is discussed when complete record of the process over a finite interval [O,t ] is available. The consistency of the estimators is established and asymptotic distributions with randorn as wel1 as non-random normings are derived.

Keywords:

• random sum central limit theorem
• random walk
• strong law of large numbers
• Toeplite lemma