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Abstract: We proved the explicit formulas in Laplace transform of the hitting times forthe birth and death processes on a denumerable state space with $\ift$ the exitor entrance boundary. This extends the well known Keilson-s theorem from finitestate space to infinite state space.We also apply these formulas to the fastest strong stationary time forstrongly ergodic birth and death processes, and obtain the explicit convergencerate in separation.



Author: Yu Gong, Yong-Hua Mao

Source: https://arxiv.org/







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