Speaker : Luisa Beghin, Dep. Statistical Sciences / Sapienza University, Rome

Time : 15:00 - 16.00 CEST (Rome/Paris)

Hosted at: SISSA, International School of Advanced Studies, Trieste, Italy

YouTube : https://youtu.be/zJewi7Uy6oc

Organizers : Pavan Pranjivan Mehta* (pavan.mehta@sissa.it) and Arran Fernandez** (arran.fernandez@emu.edu.tr)

* SISSA, International School of Advanced Studies, Italy

** Eastern Mediterranean University, Northern Cyprus

Keywords: Fractional operators, Grey Brownian motions, Incomplete gamma function, Tricomi Hypergeometric function.

Abstract: We present and analyze some stochastic processes defined in analogy with fractional Brownian motion, in infinite-dimensional white or grey-noise spaces. By means of Riemann-Liouville, Hadamard-type or general fractional operators, we extend grey Brownian motion (see e.g. [1], [2]), providing new models for anomalous diffusions. In particular, we consider the non-Gaussian process defined by means of the so-called incomplete gamma measure ([3]). Moreover, we present a Gaussian class of processes linked to the Hadamard derivatives or integrals ([4]) and to generalized fractional operators with Sonine-pair kernels ([5]).

Biography: Luisa Beghin is a full professor in Probability and Mathematical Statistics at Sapienza University in Rome. She obtained a PhD. in Methodological Statistics from Sapienza University in 2000. Her current research interests are primarily in stochastic processes linked to fractional calculus and non-local operators, Lévy processes, subordination and time-change theory.

Bibliography

[1] M. Grothaus, F., Jahnert, F. Riemann, J.L. da Silva, “Mittag-Leffler analysis I: Construction and characterization”. In Journal of Functional Analysis, 268, (7) (2015), pp. 1876-1903

[2] A. Mura, G. Pagnini. “Characterizations and simulations of a class of stochastic processes to model anomalous diffusion”. In J. Phys. A: Math. Theor., 41(28), (2008):285003, 22.

[3] L. Beghin, L. Cristofaro, J. Gajda, Non-Gaussian measures in infinite dimensional spaces: the Gamma grey noise. In Potential Analysis, 59 (2), (2023), 1-23.

[4] L. Beghin, L. Cristofaro, F. Polito, Stochastic processes related to Hadamard operators and Le Roy measures, (2024+), in preparation.

[5] L. Beghin, L. Cristofaro, Y. Mishura, A Gaussian class of processes linked to generalized fractional operators, arXiv :2309.13283, (2023) 1-39.