Lévy Processes Linked to the Lower-Incomplete Gamma Function
We start by defining a subordinator by means of the lower-incomplete gamma function. This can be considered as an approximation of the stable subordinator, easier to be handled in view of its finite activity. A tempered version is also considered in order to overcome the drawback of infinite moments...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-07-01
|
| Series: | Fractal and Fractional |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2504-3110/5/3/72 |
| _version_ | 1797519225796952064 |
|---|---|
| author | Luisa Beghin Costantino Ricciuti |
| author_facet | Luisa Beghin Costantino Ricciuti |
| author_sort | Luisa Beghin |
| collection | DOAJ |
| description | We start by defining a subordinator by means of the lower-incomplete gamma function. This can be considered as an approximation of the stable subordinator, easier to be handled in view of its finite activity. A tempered version is also considered in order to overcome the drawback of infinite moments. Then, we study Lévy processes that are 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 produces a model of anomalous diffusion, which exhibits a sub-diffusive behavior. |
| first_indexed | 2024-03-10T07:39:58Z |
| format | Article |
| id | doaj.art-b757589e44ef407996a2502dda7cd283 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-10T07:39:58Z |
| publishDate | 2021-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Fractal and Fractional |
| spelling | doaj.art-b757589e44ef407996a2502dda7cd2832023-11-22T13:09:08ZengMDPI AGFractal and Fractional2504-31102021-07-01537210.3390/fractalfract5030072Lévy Processes Linked to the Lower-Incomplete Gamma FunctionLuisa Beghin0Costantino Ricciuti1Department of Statistical Science, Sapienza University of Rome, P.le A. Moro 5, 00185 Roma, ItalyDepartment of Statistical Science, Sapienza University of Rome, P.le A. Moro 5, 00185 Roma, ItalyWe start by defining a subordinator by means of the lower-incomplete gamma function. This can be considered as an approximation of the stable subordinator, easier to be handled in view of its finite activity. A tempered version is also considered in order to overcome the drawback of infinite moments. Then, we study Lévy processes that are 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 produces a model of anomalous diffusion, which exhibits a sub-diffusive behavior.https://www.mdpi.com/2504-3110/5/3/72incomplete-gamma functionanomalous diffusionsLévy processessubordinationfractional operators |
| spellingShingle | Luisa Beghin Costantino Ricciuti Lévy Processes Linked to the Lower-Incomplete Gamma Function Fractal and Fractional incomplete-gamma function anomalous diffusions Lévy processes subordination fractional operators |
| title | Lévy Processes Linked to the Lower-Incomplete Gamma Function |
| title_full | Lévy Processes Linked to the Lower-Incomplete Gamma Function |
| title_fullStr | Lévy Processes Linked to the Lower-Incomplete Gamma Function |
| title_full_unstemmed | Lévy Processes Linked to the Lower-Incomplete Gamma Function |
| title_short | Lévy Processes Linked to the Lower-Incomplete Gamma Function |
| title_sort | levy processes linked to the lower incomplete gamma function |
| topic | incomplete-gamma function anomalous diffusions Lévy processes subordination fractional operators |
| url | https://www.mdpi.com/2504-3110/5/3/72 |
| work_keys_str_mv | AT luisabeghin levyprocesseslinkedtothelowerincompletegammafunction AT costantinoricciuti levyprocesseslinkedtothelowerincompletegammafunction |