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Conditional Processes Induced by Birth and Death Processes

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  • Masaru Iizuka
  • Matsuyo Tomisaki

Abstract

For birth and death processes with finite state space, we consider stochastic processes induced by conditioning on hitting the right boundary point before hitting the left boundary point. We call the induced stochastic processes the conditional processes. We show that the conditional processes are again birth and death processes when the right boundary point is absorbing. On the other hand, it is shown that the conditional processes do not have Markov property and they are not birth and death processes when the right boundary point is reflecting.

Suggested Citation

  • Masaru Iizuka & Matsuyo Tomisaki, 2010. "Conditional Processes Induced by Birth and Death Processes," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2010, pages 1-24, July.
    • Handle: RePEc:hin:jijmms:784567
    DOI: 10.1155/2010/784567
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