Cari colleghi,

vi annuncio che venerdì 29 Maggio 2015, alle ore 15 precise, presso la sala conferenze dell’IMATI-CNR di Pavia,

Giovanni Zanco (Università di Pisa)

terrà un seminario dal titolo:

INFINITE DIMENSIONAL METHODS FOR PATH-DEPENDENT SDES: KOLMOGOROV
EQUATIONS AND ITO FORMULAE

nell'ambito del Seminario di Matematica Applicata (IMATI-CNR e
Dipartimento di Matematica, Pavia).

Tutti gli interessati sono invitati a partecipare.

Abstract.

Path-dependent stochastic differential equations are (non-markovian)
equations whose coefficients are allowed to depend on the whole
trajectory of the solution up to the present time, and are a powerful
tool in modeling complex evolution systems with memory that appear in
finance, engineering and biology.
Even when the state space is finite dimensional, they are
intrinsecally infinite dimensional. I will show how path-dependent
SDEs can be studied in a product space framework (inspired by the
theory for delay equations) using standard differential and
topological structures. This framework is helpful to prove existence
and uniqueness of classical solutions to path-dependent
Kolmogorov-type PDEs on the space of continuous paths, to obtain
probabilistic representation formulas for such solutions and moreover
to prove Ito-type formulae for functionals of paths of continuous
semimartingales, thus providing a counterpart of the functional Ito
calculus developed by Dupire, Cont and Fournié.
It also provides an insight on the role and the analytical structure
of the so-called horizontal derivative, which is a key object in the
study of path-dependent equations.
The results I will present have been obtained in collaboration with
Franco Flandoli (Unipi) and Francesco Russo (Ensta-ParisTech).

Raffaella Carbone, PhD

Ricercatore di Probabilità e Statistica Matematica

Dipartimento di Matematica dell'Università degli Studi di Pavia