Dottore di ricerca

ciclo: XXXVI

supervisore: Luisa Beghin
co-supervisore: Prof. Da Silva

Titolo della tesi: Infinite Dimensional Analysis through Special Functions and Generalized Fractional Operators

Motivated by the results of white noise and especially Mittag-Leffler analysis, we first construct two non-Gaussian settings defined through upper-incomplete gamma function and generalized Wright functions, respectively. In both cases, we introduce the related Appell system and the spaces of test functions, as well as the distributions’ space. In the case of generalized Wright analysis, we study the Donsker’s delta and prove the existence of local times. In the second part, we introduce the so called Bernstein Gaussian processes, by defining general fractional operators and applying these in the white noise setting. By using the tools of white noise analysis, we prove the existence of the related noise and of the Ornstein-Uhlenbeck process.

Produzione scientifica

11573/1688302 - 2023 - Non-Gaussian Measures in Infinite Dimensional Spaces: the Gamma-Grey Noise
Beghin, Luisa; Cristofaro, Lorenzo; Gajda, Janusz - 01a Articolo in rivista
rivista: POTENTIAL ANALYSIS (Kluwer Academic Publishers:Journals Department, PO Box 322, 3300 AH Dordrecht Netherlands:011 31 78 6576050, EMAIL: frontoffice@wkap.nl, kluweronline@wkap.nl, INTERNET: http://www.kluwerlaw.com, Fax: 011 31 78 6576254) pp. 1-23 - issn: 0926-2601 - wos: WOS:001076761900001 (0) - scopus: 2-s2.0-85168572878 (0)

11573/1689528 - 2023 - Renewal processes linked to fractional relaxation equations with variable order
Beghin, Luisa; Cristofaro, Lorenzo; Garrappa, Roberto - 01a Articolo in rivista
rivista: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (New York: Elsevier Science Orlando Fla.: Academic Press) pp. 1-24 - issn: 0022-247X - wos: WOS:001100001600001 (0) - scopus: 2-s2.0-85173762481 (0)

11573/1676806 - 2023 - A fractional approach to study the pure-temporal Epidemic Type Aftershock Sequence (ETAS) process for earthquakes modeling
Cristofaro, L.; Garra, R.; Scalas, E.; Spassiani, I. - 01a Articolo in rivista
rivista: FRACTIONAL CALCULUS & APPLIED ANALYSIS (Sofia : Bulgarian Academy of Sciences. Institute of Mathematics and Informatics) pp. 461-479 - issn: 1311-0454 - wos: WOS:000953895200002 (1) - scopus: 2-s2.0-85150434057 (1)

11573/1549914 - 2021 - Long Memory in Earthquake Time Series: The Case Study of the Geysers Geothermal Field
Barani, S.; Cristofaro, L.; Taroni, M.; Gil-Alana, L. A.; Ferretti, G. - 01a Articolo in rivista
rivista: FRONTIERS IN EARTH SCIENCE (Lausann : Frontiers Media S.A., 2013-) pp. - - issn: 2296-6463 - wos: WOS:000641032800001 (0) - scopus: 2-s2.0-85104556355 (0)

11573/1549916 - 2020 - Modelling stock market data in China: Crisis and Coronavirus
Cristofaro, L.; Gil-Alana, L. A.; Chen, Z.; Wanke, P. - 01a Articolo in rivista
rivista: FINANCE RESEARCH LETTERS (Elsevier) pp. 101865- - issn: 1544-6123 - wos: WOS:000663415300057 (2) - scopus: 2-s2.0-85097189839 (2)

11573/1549918 - 2020 - Long memory and time trends in particulate matter pollution (PM2.5 and PM10) in the 50 U.S. States
Gil-Alana, L. A.; Yaya, O. S.; Awolaja, O. G.; Cristofaro, L. - 01a Articolo in rivista
rivista: JOURNAL OF APPLIED METEOROLOGY AND CLIMATOLOGY (Boston, MA : American Meteorological Society, 2006-) pp. 1351-1367 - issn: 1558-8424 - wos: WOS:000589933400005 (4) - scopus: 2-s2.0-85090027758 (4)

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