On transient probabilities of fractional birth-death process

Article Type

Research Article

Publication Title

Alea

Abstract

We study a fractional birth-death process with state dependent birth and death rates. It is defined using a system of fractional differential equations that generalizes the classical birth-death process introduced by Feller (1939). We obtain the closed form expressions for its transient probabilities using Adomian decomposition method. In this way, we obtain the unknown transient probabilities for the classical birth-death process (see Feller (1968), p. 454). Its various distributional properties are studied. For linear birth and death rates, the obtained results are verifi with the existing results. Also, we discuss the cumulative births in fractional linear birth-death process. Later, we consider a time-changed linear birth-death process for which we obtain an asymptotic behaviour of the distribution function of extinction time at zero.

First Page

1085

Last Page

1110

DOI

10.30757/ALEA.v22-43

Publication Date

1-1-2025

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