Limit theorems for the fractional nonhomogeneous Poisson process
Copyright policy )Limit theorems for the fractional nonhomogeneous Poisson process
AbstractThe fractional nonhomogeneous Poisson process was introduced by a time change of the nonhomogeneous Poisson process with the inverseα-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.
- Cardiff University United Kingdom
- University of Sussex United Kingdom
- Sapienza University of Rome Italy
QA0274, Functional limit theorems; invariance principles, Lévy process, Probability (math.PR), Central limit and other weak theorems, subordination, Poisson process, fractional point processes, additive process, QA273, time change, additive process; Fractional point processes; limit theorem; Lévy process; Poisson process; subordination; time change, FOS: Mathematics, limit theorem, Point processes (e.g., Poisson, Cox, Hawkes processes), Mathematics - Probability
QA0274, Functional limit theorems; invariance principles, Lévy process, Probability (math.PR), Central limit and other weak theorems, subordination, Poisson process, fractional point processes, additive process, QA273, time change, additive process; Fractional point processes; limit theorem; Lévy process; Poisson process; subordination; time change, FOS: Mathematics, limit theorem, Point processes (e.g., Poisson, Cox, Hawkes processes), Mathematics - Probability
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