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
to 15:15