Lévy processes linked to the lower-incomplete gamma function

2021/06/23 by Luisa Beghin, Beghin, Luisa, Costantino Ricciuti +1
Mathematics · #26A33 #33B20 #34A08 #34A08 26A33 #60G51 #60J65 #FOS: Mathematics #Probability (math.PR) #math.PR #msc:26A33 #msc:33B20 #msc:34A08 #msc:60G51 #msc:60J65

paper · pdf · doi:10.48550/arxiv.2106.12201

17 pages

arxiv created 2021/06/23 · arxiv updated 2021/06/24

Abstract

We start by defining a subordinator by means of the lower-incomplete gamma function. It can be considered as an approximation of the stable subordinator, easier to be handled thank to its finite activity. A tempered version is also considered in order to overcome the drawback of infinite moments. Then, we study Lévy processes time-changed by these subordinators, with particular attention to the Brownian case. An approximation of the fractional derivative (as well as of the fractional power of operators) arises from the analysis of governing equations. Finally, we show that time-changing the fractional Brownian motion gives a model of anomalous diffusion, which exhibits a sub-diffusive behavior.

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