FABRIZIO CINQUE

Dottore di ricerca

ciclo: XXXVI



Titolo della tesi: Multidimensional finite-velocity stochastic motions and their fractional versions

We study multidimensional motions with finite velocities, generalizations of the well-known telegraph process. We begin by presenting orthogonal motions moving in $\mathbb{R}^2$ and $\mathbb{R}^3$ and governed by a non-homogeneous Poisson process. One of the main result is that the planar process can be represented as the linear trasformations of two independent one-dimensional telegraph processes. We then consider processes in higher dimensions, studying in depth the minimal motions, obtaining the form of the distribution inside the support and on its border. We also consider more general motions, focusing also on the connections between motions developing in different dimensions. Finally, we study Dzherbasyhan-Caputo fractional Cauchy problems of higher order, obtaining also some interesting results involving the inverses of stable subordinators. The study of fractional problems permits us to show fractional versions of muldimensional random motions.

Produzione scientifica

11573/1717069 - 2024 - Multidimensional random motions with a natural number of finite velocities
Cinque, F.; Cintoli, M. - 01a Articolo in rivista
rivista: ADVANCES IN APPLIED PROBABILITY (Applied Probability:School of Mathematics and Statistics, The University, Sheffield S3 7RH United Kingdom:EMAIL: s.c.boyles@sheffield.ac.uk, INTERNET: http://www.shef.ac.uk/uni/companies/apt, Fax: 011 44 114 2729782) pp. 1-31 - issn: 0001-8678 - wos: WOS:001192281300001 (0) - scopus: 2-s2.0-85187272081 (1)

11573/1717068 - 2024 - Analysis of fractional Cauchy problems with some probabilistic applications
Cinque, Fabrizio; Orsingher, Enzo - 01a Articolo in rivista
rivista: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS (New York: Elsevier Science Orlando Fla.: Academic Press) pp. - - issn: 0022-247X - wos: WOS:001184720300001 (1) - scopus: 2-s2.0-85187283760 (1)

11573/1666280 - 2023 - Stochastic Dynamics of Generalized Planar Random Motions with Orthogonal Directions
Cinque, F; Orsingher, E - 01a Articolo in rivista
rivista: JOURNAL OF THEORETICAL PROBABILITY (Plenum Press:Book Customer Service, 233 Spring Street:New York, NY 10013:(212)620-8471, (212)620-8000, EMAIL: info@plenum.com, INTERNET: http://www.plenum.com, Fax: (212)807-1047) pp. 1-33 - issn: 0894-9840 - wos: WOS:000907816600001 (6) - scopus: 2-s2.0-85145548121 (6)

11573/1683808 - 2023 - Random motions in R3 with orthogonal directions
Cinque, Fabrizio; Orsingher, Enzo - 01a Articolo in rivista
rivista: STOCHASTIC PROCESSES AND THEIR APPLICATIONS (Elsevier BV:PO Box 211, 1000 AE Amsterdam Netherlands:011 31 20 4853757, 011 31 20 4853642, 011 31 20 4853641, EMAIL: nlinfo-f@elsevier.nl, INTERNET: http://www.elsevier.nl, Fax: 011 31 20 4853598) pp. 173-200 - issn: 0304-4149 - wos: WOS:000988359100001 (4) - scopus: 2-s2.0-85152595404 (4)

11573/1617585 - 2022 - On the sum of independent generalized Mittag–Leffler random variables and the related fractional processes
Cinque, F. - 01a Articolo in rivista
rivista: STOCHASTIC ANALYSIS AND APPLICATIONS (Marcel Dekker Incorporated:270 Madison Avenue:New York, NY 10016:(800)228-1160, (212)696-9000, EMAIL: bookorders@dekker.com, INTERNET: http://www.dekker.com, Fax: (212)685-4540) pp. 103-117 - issn: 0736-2994 - wos: WOS:000624996000001 (5) - scopus: 2-s2.0-85112841471 (4)

11573/1617649 - 2022 - A note on the conditional probabilities of the telegraph process
Cinque, F. - 01a Articolo in rivista
rivista: STATISTICS & PROBABILITY LETTERS (Elsevier BV:PO Box 211, 1000 AE Amsterdam Netherlands:011 31 20 4853757, 011 31 20 4853642, 011 31 20 4853641, EMAIL: nlinfo-f@elsevier.nl, INTERNET: http://www.elsevier.nl, Fax: 011 31 20 4853598) pp. 109431- - issn: 0167-7152 - wos: WOS:000789676400009 (0) - scopus: 2-s2.0-85125443040 (4)

11573/1662889 - 2022 - Reflection principle for finite-velocity random motions
Cinque, Fabrizio - 01a Articolo in rivista
rivista: JOURNAL OF APPLIED PROBABILITY (Applied Probability:School of Mathematics and Statistics, The University, Sheffield S3 7RH United Kingdom:EMAIL: s.c.boyles@sheffield.ac.uk, INTERNET: http://www.shef.ac.uk/uni/companies/apt, Fax: 011 44 114 2729782) pp. 1-14 - issn: 0021-9002 - wos: WOS:000981937700008 (1) - scopus: 2-s2.0-85159282687 (1)

11573/1633382 - 2021 - On the exact distributions of the maximum of the asymmetric telegraph process
Cinque, F.; Orsingher, E. - 01a Articolo in rivista
rivista: STOCHASTIC PROCESSES AND THEIR APPLICATIONS (Elsevier BV:PO Box 211, 1000 AE Amsterdam Netherlands:011 31 20 4853757, 011 31 20 4853642, 011 31 20 4853641, EMAIL: nlinfo-f@elsevier.nl, INTERNET: http://www.elsevier.nl, Fax: 011 31 20 4853598) pp. 601-633 - issn: 0304-4149 - wos: WOS:000711200200003 (8) - scopus: 2-s2.0-85116922429 (9)

11573/1617599 - 2020 - On the distribution of the maximum of the telegraph process
Cinque, F.; Orsingher, E. - 01a Articolo in rivista
rivista: THEORY OF PROBABILITY AND MATHEMATICAL STATISTICS (American Mathematical Society:PO Box 6248:Providence, RI 02940:(800)321-4267, (401)455-4000, EMAIL: cust-serv@ams.org, gma@math.ams.org, INTERNET: http://www.ams.org, Fax: (401)331-3842) pp. 73-95 - issn: 0094-9000 - wos: WOS:000640241800005 (5) - scopus: 2-s2.0-85098429501 (6)

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