Weak convergence of conditioned birth-death processes in discrete time

Coolen-Schrijner, Pauline and Doorn van, Erik A. (1997) Weak convergence of conditioned birth-death processes in discrete time. Journal of Applied Probability, 34 (1). pp. 46-53. ISSN 0021-9002

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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.
Item Type:	Article
Copyright:	© 1997 Applied Probability Trust
Faculty:	Electrical Engineering, Mathematics and Computer Science (EEMCS)
Research Group:	Statistics and Probability (SP)
Link to this item:	http://purl.utwente.nl/publications/62355
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