FractionalLT_AP.pdf (614.59 kB)
Limit theorems for the fractional non-homogeneous Poisson process
journal contribution
posted on 2023-06-09, 16:41 authored by Nikolai Leonenko, Enrico Scalas, Mailan TrinhThe fractional nonhomogeneous Poisson process was introduced by a time change of the nonhomogeneous Poisson process with the inverse a-stable subordinator. We propose a similar definition for the (nonhomogeneous) fractional compound Poisson process. We give both finite-dimensional and functional limit theorems for the fractional nonhomogeneous Poisson process and the fractional compound Poisson process. The results are derived by using martingale methods, regular variation properties and Anscombe’s theorem. Eventually, some of the limit results are verified in a Monte Carlo simulation.
History
Publication status
- Published
File Version
- Accepted version
Journal
Journal of Applied ProbabilityISSN
0021-9002Publisher
Cambridge University PressExternal DOI
Issue
1Volume
56Page range
246-264Department affiliated with
- Mathematics Publications
Research groups affiliated with
- Probability and Statistics Research Group Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2019-01-31First Open Access (FOA) Date
2019-04-11First Compliant Deposit (FCD) Date
2019-01-30Usage metrics
Categories
No categories selectedKeywords
Licence
Exports
RefWorks
BibTeX
Ref. manager
Endnote
DataCite
NLM
DC