The fractional non-homogeneous Poisson process
Copyright policy )The fractional non-homogeneous Poisson process
We introduce a non-homogeneous fractional Poisson process by replacing the time variable in the fractional Poisson process of renewal type with an appropriate function of time. We characterize the resulting process by deriving its non-local governing equation. We further compute the first and second moments of the process. Eventually, we derive the distribution of arrival times. Constant reference is made to previous known results in the homogeneous case and to how they can be derived from the specialization of the non-homogeneous process.
15 pages
- Cardiff University United Kingdom
- Sapienza University of Rome Italy
- Department of Mathematics
- University of Sussex United Kingdom
Fractional point processes; Lévy processes; Subordination; Time-change, Probability (math.PR), time-change, Fractional processes, including fractional Brownian motion, subordination, fractional point processes, 60G55, 60K05, 60G22, QA273, Lévy processes, FOS: Mathematics, Point processes (e.g., Poisson, Cox, Hawkes processes), QA, Mathematics - Probability
Fractional point processes; Lévy processes; Subordination; Time-change, Probability (math.PR), time-change, Fractional processes, including fractional Brownian motion, subordination, fractional point processes, 60G55, 60K05, 60G22, QA273, Lévy processes, FOS: Mathematics, Point processes (e.g., Poisson, Cox, Hawkes processes), QA, Mathematics - Probability
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).32 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Top 10%
Citations provided by BIP!Popularity provided by BIP!