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- W1640808034 abstract "We introduce and study fractional generalizations of the well-known Gamma process, in the following sense: the corresponding densities are proved to satisfy the same differential equation as the usual Gamma process, but with the shift operator replaced by its fractional version of order ν > 0. In the case ν > 1, the solution corresponds to the density of a Gamma process time-changed by an independent stable subordinator of index 1/ν. For ν less than one an analogous result holds, with the subordinator replaced by the inverse. In this case the fractional Gamma process is proved to be a non-stationary version of the standard one, with power law behavior of the expected value. Hence it can be considered a useful tool in modelling stochastic deterioration in the non-linear cases, a situation which often occurs in real data (see i.e., [42] and the references therein).As a consequence of the previous results, the fractional generalizations of some Gamma subordinated processes (i.e. the Variance Gamma, the Geome..." @default.
- W1640808034 created "2016-06-24" @default.
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- W1640808034 date "2015-08-05" @default.
- W1640808034 modified "2023-09-26" @default.
- W1640808034 title "Fractional Gamma and Gamma-Subordinated Processes" @default.
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- W1640808034 doi "https://doi.org/10.1080/07362994.2015.1053615" @default.
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