# Weak convergence of conditioned birth-death processes in discrete time

Pauline Coolen-Schrijner, Erik A. van Doorn

1 Citation (Scopus)

### Abstract

We consider a discrete-time birth-death process on the nonnegative integers with -1 as an absorbing state and study the limiting behaviour as $n \to \infty$ of the process conditioned on nonabsorption until time $n$. By proving that a condition recently proposed by Martinez and Vares is vacuously true, we establish that the conditioned process is always weakly convergent when all self-transition probabilities are zero. In the aperiodic case we obtain a necessary and sufficient condition for weak convergence.
Original language English 46-53 12 Journal of applied probability 34 34 https://doi.org/10.2307/3215173 Published - 1997

### Keywords

• EWI-12860
• IR-62355
• METIS-140771