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HITTING TIME DISTRIBUTIONS FOR BIRTH–DEATH PROCESSES WITH BILATERAL ABSORBING BOUNDARIES

  • Yong-Hua Mao (a1) and Chi Zhang (a2)

Abstract

For the birth–death process on a finite state space with bilateral boundaries, we give a simpler derivation of the hitting time distributions by h-transform and φ-transform. These transforms can then be used to construct a quick derivation of the hitting time distributions of the minimal birth–death process on a denumerable state space with exit/regular boundaries.

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