Stochastic calculus for non-semimartingales in Banach spaces and an infinite dimensional PDE
Event details
| Date | 23.03.2012 |
| Hour | 10:15 › 11:15 |
| Speaker | Cristina Di Girolami |
| Location | |
| Category | Conferences - Seminars |
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 thespace 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 pathdependent 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.
This is a joint work with Francesco Russo (ENSTA ParisTech).
(for instance Dirichlet, weak Dirichlet), it is possible to represent a large class of pathdependent 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.
This is a joint work with Francesco Russo (ENSTA ParisTech).
Practical information
- General public
- Free
Organizer
- CIB
Contact
- Isabelle Derivaz-Rabii