On a fractional linear birth-death process

By Enzo Orsingher, Federico Polito. 2011

47 citations recorded by the source corpus.

In this paper, we introduce and examine a fractional linear birth–death process N�(t), t > 0, whose fractionality is obtained by replacing the time derivative with a fractional derivative in the system of difference-differential equations governing the state probabilities p �(t), t > 0, k � 0. We present a subordination relationship connecting N�(t), t > 0, with the classical birth–death process N(t), t > 0, by means of the time process T2�(t), t > 0, whose distribution is related to a time-fractional diffusion equation. We obtain explicit formulas for the extinction probability p �(t) and the state probabilities

Subfields: Applied Mathematics, Modeling and Simulation, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/4560e411abee69da0ce22f112fe82e707dda4d67