Reproduction of initial distributions from the first hitting time distribution for birth-and-death processes

Kosuke Yamato; Kouji Yano

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arXiv · 2203.12260

Reproduction of initial distributions from the first hitting time distribution for birth-and-death processes

Kosuke Yamato·Kouji Yano

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Abstract

For birth-and-death processes, we show that every initial distribution is reproduced from the first hitting time distribution. The reproduction is done by applying to the distribution function a differential operator defined through the eigenfunction of the generator. Using the spectral theory for generalized second-order differential operators, we study asymmetric random walks.

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Kosuke Yamato, Kouji Yano. 2022-03-23. Reproduction of initial distributions from the first hitting time distribution for birth-and-death processes. https://arxiv.org/abs/2203.12260

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