P-Thinned Gamma Process and Corresponding Random Walk
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.
KeywordsRandom walk Gamma process Mixed distribution Convolutions Zero-inflation
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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