In this paper, we investigate on a class of time-inhomogeneous birth-death chains obtained by applying the composition method to two time-inhomogeneous double-ended chains. Then, we consider the corresponding restricted birth-death process, with zero reflecting boundary. Finally, starting from the restricted process, we construct a time-inhomogeneous BD chain symmetric with respect to zero-state. We obtain closed form expressions for the transition probabilities and for the conditional moments; furthermore, the first-passage-time problem is also taken in consideration. Finally, various numerical computations are performed for periodic intensity functions.

On a class of birth-death processes with time-varying intensity functions

Virginia Giorno;Amelia Giuseppina Nobile
2020

Abstract

In this paper, we investigate on a class of time-inhomogeneous birth-death chains obtained by applying the composition method to two time-inhomogeneous double-ended chains. Then, we consider the corresponding restricted birth-death process, with zero reflecting boundary. Finally, starting from the restricted process, we construct a time-inhomogeneous BD chain symmetric with respect to zero-state. We obtain closed form expressions for the transition probabilities and for the conditional moments; furthermore, the first-passage-time problem is also taken in consideration. Finally, various numerical computations are performed for periodic intensity functions.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11386/4737671
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