title:
Discrete approximation of stochastic integrals and fractional smoothness in terms of Malliavin calculus |
name:
Laukkarinen |
first name:
Eija
|
location/conference:
levy10
|
abstract:
We consider discrete approximation of certain stochastic
integrals with respect to the stochastic exponential of a L\'evy
process. The convergence rate as the number of discretisation
points increases depends on the fractional smoothness of the
stochastic integral and the choice of the discretisation points.
The fractional Sobolev spaces are obtained by real interpolation
between the space of square integrable random variables and the
Malliavin Sobolev space. The fractional Sobolev spaces are
considered from various aspects. The work has been partly done in
collaboration with Ch. Geiss and S. Geiss. |