Weak convergence of conditioned birth-death processes in discrete time


Coolen-Schrijner, Pauline and Doorn, Erik A. van (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.
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Copyright:© 1997 Applied Probability Trust
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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