*Tid:* **19 april 1999 kl 1515-1700**

*Plats :* **Seminarierummet 3733**, Institutionen för
matematik, KTH, Lindstedts väg 25, plan 7. Karta!

*Föredragshållare:*
**
Laurent Decreusefond, Ecole nationale supérieure des
télécommunications, Paris.
**

**Titel:** **
A functional central limit theorem for fractional Brownian motion.
**

*Sammanfattning: *

Abstract in Postscript format

A result of Fouque (1984) stands that for a standard
Brownian motion *B*, the
sequence of -valued processes

where are independent copies of *B*,
converges in distribution to a generalized Ornstein-Uhlenbeck
process. The main ingredients in this work are general result on
convergence in nuclear spaces and the Itô
formula. The problem addressed here is to generalize this result when
the standard Brownian motion is replaced by a fractional Brownian
motion of Hurst index in denoted by Since is
not a semi-martingale and that an Itô formula does not exist for
when the method of Fouque can not be straightforwardly applied.
The difficulty is bypassed by considering a sample-path
valued semi-martingale , namely
(where is defined in order that
)
which is such that and for which one can write an
Itô formula. The methods of Fouque are then
applicable to so that we can solve our original problem and
show that
converges weakly in to a time changed
generalized Ornstein-Uhlenbeck process.
Till seminarielistan

To the list of
seminars