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Weak convergence of conditioned birth and death processes
Part of
- Markov processes
G. O. Roberts, S. D. Jacka
Journal:

Journal of Applied Probability / Volume 31 / Issue 1 / March 1994

Published online by Cambridge University Press:

14 July 2016, pp. 90-100

Print publication:

March 1994
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We consider the problem of conditioning a non-explosive birth and death process to remain positive until time T, and consider weak convergence of this conditional process as T → ∞. By a suitable almost sure construction we prove weak convergence. The almost sure construction used is of independent interest but relies heavily on the strong monotonic properties of birth and death processes.

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Weak convergence of conditioned birth and death processes