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- W2051290037 abstract "We consider a fractional version of the classical nonlinear birth process of which the Yule–Furry model is a particular case. Fractionality is obtained by replacing the first order time derivative in the difference-differential equations which govern the probability law of the process with the Dzherbashyan–Caputo fractional derivative. We derive the probability distribution of the number $mathcal{N}_{nu}(t)$ of individuals at an arbitrary time $t$. We also present an interesting representation for the number of individuals at time $t$, in the form of the subordination relation $mathcal{N}_{nu}(t)=mathcal{N}(T_{2nu}(t))$, where $mathcal{N}(t)$ is the classical generalized birth process and $T_{2ν}(t)$ is a random time whose distribution is related to the fractional diffusion equation. The fractional linear birth process is examined in detail in Section 3 and various forms of its distribution are given and discussed." @default.
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- W2051290037 date "2010-08-01" @default.
- W2051290037 modified "2023-09-30" @default.
- W2051290037 title "Fractional pure birth processes" @default.
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- W2051290037 doi "https://doi.org/10.3150/09-bej235" @default.
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