UNIVERSITA' DI SALERNO

Dipartimento di Matematica

 AVVISO DI SEMINARIO

Il dott. Costantino RICCIUTI (Università di Roma "La Sapienza", Dipartimento di Scienze Statistiche) terrà, giovedì 20 luglio, alle ore 12:00, presso la Sala Riunioni dell'Edificio F2 (piano 1, stanza 36), un seminario dal titolo:

Multivariate subordination, generalized fractional equations and anomalous diffusion

Gli interessati sono cordialmente invitati a partecipare,   

Antonio Di Crescenzo

Barbara Martinucci

 Alessandra Meoli

  Serena Spina

Link su Teams: 

https://teams.microsoft.com/l/meetup-join/19%3a6hfHOOIVt89PyLIJDpqXis553z6pgGL9RMiVIQJWO201%40thread.tacv2/1689614109773?context=%7b%22Tid%22%3a%22c30767db-3dda-4dd4-8a4d-097d22cb99d3%22%2c%22Oid%22%3a%2261e4e421-60a6-4cb9-8153-d04cb91c1edf%22%7d

Abstract

In this talk we consider multiparameter Levy processes and multivariate subordinators in the sense of [1]. These models are not as well-known as other multiparameter extensions of Levy processes, such as the Brownian sheet or the Additive processes, yet they lead to a number of results that are interesting both in Analysis and Statistical Physics. Inspired by [1], we develop a theory for subordination of random fields, also providing a Phillips-type formula. This allows us to obtain stochastic solutions to systems of differential or integro-differential equations. We also study the composition of multiparameter Levy processes by means of the so-called "inverses" of multivariate subordinators. The resulting processes have interesting long range dependence properties and are governed by non local equations (potentially exhibiting fractional operators). As a byproduct, we present a model of anomalous diffusion where the particle moves within anisotropic media. The results presented in this talk are taken from [2] and [3].

[1] O. Barndorff-Nielsen; J. Pedersen; K. Sato. Multivariate subordination, self-decomposability and stability. Adv. in Appl. Probab. 33 (1), 160-187, 2001.

[2] L. Beghin; C. Macci; C. Ricciuti. Random time-change with inverses of multivariate subordinators: Governing equations and fractional dynamics. Stoch. Proc. Appl. 130(10), pp. 6364-6387, 2020.

[3] F. Iafrate; C. Ricciuti. Some families of random fields related to multiparameter Levy processes. arXiv preprint arXiv:2211.00346, 2022.