Abstract
P-thinned Gamma processes could be considered as a particular case of renewal processes which inter-renewal times are zero-inflated Gamma distributed. This paper considers also the difference between two, not obligatory identically distributed, processes which time intersections coincide in distribution with convolutions of zero-inflated Gamma distributed random variables. The idea comes from the Variance-Gamma model which is defined as Gamma time changed Wiener processes and is stochastically equivalent to a difference between two independent Gamma processes. The main properties and numerical characteristics of the resulting process are obtained. Simulation illustrates the theoretical results.
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Notes
- 1.
These measures of heavy-tailedness were introduced and partially investigated in Jordanova and Petkova [4].
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Acknowledgements
The authors were supported by the bilateral projects Bulgaria - Austria, 2016–2019, Feasible statistical modelling for extremes in ecology and finance, Contract number 01/8, 23/08/2017 and WTZ Project No. BG 09/2017.
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Jordanova, P., Stehlík, M. (2019). P-Thinned Gamma Process and Corresponding Random Walk. In: Dimov, I., Faragó, I., Vulkov, L. (eds) Finite Difference Methods. Theory and Applications. FDM 2018. Lecture Notes in Computer Science(), vol 11386. Springer, Cham. https://doi.org/10.1007/978-3-030-11539-5_33
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