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