AVVISO di SEMINARIO

Title: Non-gaussian processes linked to H-functions

Prof.ssa Luisa Beghin

Università di Roma La Sapienza

Abstract. In the context of non-Gaussian analysis, Schneider [1] introduced grey noise measures, built upon Mittag-Leffler functions; analogously, grey Brownian motion and its generalizations were constructed (see, for example, [2], [3], [4], [5]).

In [6], we construct and study a new non-Gaussian measure, by means of the incomplete-gamma function (exploiting its complete monotonicity).The related generalized processes, in the infinite dimensional setting, are also defined and, through the use of the Riemann-Liouville fractional operators, the (possibly tempered) Gamma-grey Brownian motion is consequently introduced. All the above mentioned processes allow modeling anomalous diffusions, mimicking the procedures of classical stochastic calculus. Finally, we present the extensions of the previous results obtained by means of the Fox H-functions, which generalize both the Mittag-Leffler and the incomplete-gamma functions (under appropriate assumptions). (This is a joint work with L. Cristofaro)

[1] W.R. Schneider, Grey noise, in Ideas and Methods in Mathematical Analysis, Stochastics and Applications, vol. I, S. Albeverio, J.E. Fenstad, H. Holden, T. Lindstrom, eds., Cambridge University Press, Cambridge, 1990, 261-282. [2] A. Mura, G. Pagnini, Characterizations and simulations of a class of stochastic processes to model anomalous diffusion, Journal of Physics A: Math. Theor., 41, 2008, 285003, 22 p. [3] W. Bock, S. Desmettre, J.L. da Silva, Integral representation of generalized grey Brownian motion, Stochastics, 92 (4), 2020, 552-565. [4] J.L. da Silva, M. Erraoui, Generalized grey Brownian motion local time: existence and weak approximation, Stochastics, 87 (2), 2015, 347-361. [5] J.L. da Silva, M. Erraoui, Singularity of generalized grey Brownian motion and time-changed Brownian motion, AIP Conference Proceedings, vol. 2286, (1), 2020, article id.020002. [6] L. Beghin, L. Cristofaro, J. Gajda, Non-gaussian measures in infinite dimensional spaces: the gamma-grey noise, 2022, arXiv 2207.13609, submitted.

Il seminario si terrà il giorno 13 Settembre 2022 ore 11:00 nella Aula E terzo livello del Dipartimento Matematica e Applicazioni, Università di Napoli FEDERICO II, Complesso di Monte Sant'Angelo, Via Cintia, Napoli.

Link al seminario su Teams:

https://teams.microsoft.com/l/meetup-join/19%3aMQ4RZDBo_0G-K_PHxKtktVYAczOGb...

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