Continuous affine Volterra processes: Ergodicity, statistics and regularity of the occupation measure

Seminario periodico del Dipartimento di Matematica
10 novembre 2023
Orario di inizio 
PovoZero - Via Sommarive 14, Povo (Trento)
Aula seminari "1" (Povo 0) e via Zoom (contattare per le credenziali)
Organizzato da: 
Dipartimento di Matematica
Comunità universitaria
Comunità studentesca UniTrento
Ingresso libero
Prof. Luigi Amedeo Bianchi, Prof. Stefano Bonaccorsi, Prof. Michele Coghi
Università degli Studi Trento 38123 Povo (TN) - Staff Dipartimento di Matematica
+39 04 61/281508-1625-1701-3898-1980-1511
Martin Friesen (Dublin City University)


We study limit distributions, stationary processes, and ergodicity for continuous affine Volterra processes. Firstly, we prove the existence of limit distributions and stationary processes for affine Volterra processes on $\R_+^m$ obtained from

  X_t = x_0 + \int_0^t k(t-s)(b+\beta X_s)ds + \int_0^t

where $\sigma(x) = \mathrm{diag}(\sigma_1 \sqrt{x_1}, \dots, \sigma_m \sqrt{x_m})$. Although the process is non-markovian, its limit distribution is independent of the initial state $x_0$ if and only if $k \not \in L^1(\R_+)$. Afterward, we prove the law-of-large numbers and deduce that the corresponding stationary process is ergodic and mixing.

As an application we consider the maximum-likelihood estimation of the drift parameter $b$ for continuous and discrete high-frequency observations. In the second part of this talk we address the behaviour of the process at the boundary in terms of regularity of occupation measures at the boundary of the state space.


This talk is partially based on joint works with Mohamed Ben Alaya and Pen Jin.