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

Stochastic Analysis Seminar Series


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)."



Monday, November 18, 2013 - 14:15
to 15:15