Seminar

A class of fractional Ornstein-Uhlenbeck processes mixed with a Gamma distribution

Seminario periodico del Dipartimento di Matematica
3 March 2022
Start time 
4:00 pm
PovoZero - Via Sommarive 14, Povo (Trento)
L'evento si terrà in aula seminari "-1" - Povo 0 e online tramite la piattaforma Zoom
Organizer: 
Dipartimento di Matematica
Target audience: 
University community
UniTrento students
Attendance: 
Free
Online
Contact person: 
Prof. Stefano Bonaccorsi, dott. Michele Coghi
Contact details: 
Università degli Studi Trento 38123 Povo (TN) - Staff Dipartimento di Matematica
+39 04 61/281508-1625-1701-3898-1980
Speaker: 
Stefano Bonaccorsi (Università di Trento)

Abstract:

We consider a sequence of fractional Ornstein-Uhlenbeck processes, that are defined as solutions of a family of stochastic Volterra equations with kernel given by the Riesz derivative kernel, and leading coefficients given by a sequence of independent Gamma random variables.

We construct a new process by taking the empirical mean of this sequence. In our framework, the processes involved are not Markovian, hence the analysis of their asymptotic behaviour requires some ad hoc construction.

In our main result, we prove the almost sure convergence in the space of trajectories of the empirical means to a given Gaussian process, which we characterize completely.

Based on a joint work with Luigi Amedeo Bianchi and Luciano Tubaro.