Uniform Convergence Rates for Birth and Death Processes

Yong-Hua Mao, Chi Zhang

2017, v.23, №3, 467-484

ABSTRACT

For the birth and death process with entrance boundary or the maximal birth and death process with regular boundary,
the uniformly exponential convergence rate in total variation equals the Neumann spectral gap, and
the uniformly exponential convergence rate in separation
lies between the Neumann spectral gap and the Dirichlet spectral gap.

Keywords: birth and death process, eigenvalues, hitting time, strong ergodicity, strong stationary time, separation

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