# Title "Stochastic calculus for non-semimartingales in Banach spaces, an infinite dimensional PDE and some stability results".

**Stochastic Analysis Seminar Series**

**Abstract:**

**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)."**

Location: | |

Speaker(s): | CRISTINA DI GIROLAMI |

Date: | Monday, November 18, 2013 - 14:15 |