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- W1988408512 abstract "The usual model for (Poissonian) linear birth–death processes is extended to multiple birth–death processes with fractional birth probabilities in the form λi(Δt)α+o((Δt)α, 0<α<1. The probability generating function for the time dependent population size is provided by a fractional partial differential equation. The solution of the latter is obtained and comparison with the usual model is made. The probability of ultimate extinction is obtained. One considers the special case of fractional Poissonian processes with individual arrivals only, and then one outlines basic results for continuous processes defined by fractional Poissonian noises. The key is the Taylor’s series of fractional order f(x+h)=Eα(hαDxα)f(x), where Eα(·) is the Mittag–Leffler function, and Dxα is the modified Riemann–Liouville fractional derivative, as previously introduced by the author." @default.
- W1988408512 created "2016-06-24" @default.
- W1988408512 creator A5015937306 @default.
- W1988408512 date "2010-12-01" @default.
- W1988408512 modified "2023-10-02" @default.
- W1988408512 title "Fractional multiple birth–death processes with birth probabilities λi(Δt)α+o((Δt)α)" @default.
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- W1988408512 doi "https://doi.org/10.1016/j.jfranklin.2010.09.004" @default.
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