Domani 6 Febbraio, alle ore 15,
presso il Dipartimento di
Matematica e Applicazioni dell'Università di Milano-Bicocca, via Cozzi, 55, Edificio U5, stanza 2107 (secondo piano),
la
Dott.ssa Cristina di Girolami, Università G. D'Annunzio di Chieti-Pescara,
terrà un seminario dal titolo
"Stochastic calculus in Banach
spaces, an infinite dimensional PDE and stability results"
This talk develops some aspects of stochastic calculus via regularization
for processes with values in a general Banach space B.
A new concept of quadratic variation which depends on a
particular subspace is introduced. An Itô formula and stability results for processes admitting this kind of quadratic variation
are presented. Particular interest is devoted to the case when B is the space of real continuous functions defined on
[-T,0], T>0 and the process is the window process X(•) associated with a continuous real process X which, at time t, it
takes into account the past of the process. If X is a finite quadratic variation process (for instance Dirichlet,
weak Dirichlet), it is possible to represent a large class of path-dependent random variable h as a real number plus a real
forward integral in a semiexplicite form.
This representation result of h makes use of a functional solving an infinite
dimensional partial differential equation.
This decomposition generalizes, in some cases, the Clark-Ocone formula
which is true when X is
the standard Brownian motion W. Some stability results will be given explicitly.
This is a joint work with Francesco Russo (ENSTA ParisTech
Paris).
Tutti gli interessati sono invitati a partecipare.
Cordiali saluti,
Federica Masiero