Tid: 14 maj 2001 kl 1515-
Plats : Seminarierummet 3733, Institutionen för matematik, KTH, Lindstedts väg 25, plan 7. Karta!
Vid seminariet måndagen den 14 maj 2001 kl. 15.15 diskuteras Henrik Hults avhandling för tekn.-lic.-examen:
Approximating some Volterra type Stochastic Integrals with Applications to Parameter Estimation.
Inbjuden diskutant är professor Svante Janson, Matematik, Uppsala universitet.
Plats: Seminarierum 3733, Institutionen för matematik, KTH, Lindstedtsvägen 25, plan 7.
Abstract:
We use a general representation of continuous Gaussian processes as the limit of a sequence of processes in the associated reproducing kernel Hilbert space, to Gaussian processes represented as Volterra type stochastic integrals with respect to Brownian motion, including the fractional Brownian motion. As special cases of this representation we obtain, for example, the Karhunen-Loève decomposition for standard Brownian motion and a wavelet representation for fractional Brownian motion. We also show how the representation can be used to estimate parameters. In particular we derive an estimator for the mean-reverting parameter in an Ornstein-Uhlenbeck process driven by a fractional Brownian motion.
Report: