Abstract
A spatial symmetry property of a two-dimensional birth–death process X(t) with constant rates is exploited in order to obtain closed-form expressions for first-passage-time densities through straight-lines x 2 = x 1 + r and for the related taboo transition probabilities. An analogous study is performed on a birth–death process with state-dependent rates that is similar to X(t) in the sense that the ratio of their transition functions is time independent. Examples of applications to double-ended queues and stochastic neuronal modeling are also provided.
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