KTH"

Tid: 23 januari 2001 kl 1630-

Plats : Matematisk statistiks fikarum (Rum 333), Institutionen för matematik, SU, hus 6 i Kräftriket, Roslagsvägen 101. (OBS! Tid och plats!)

Föredragshållare: Henrik Hult, Matematisk statistik, Kungliga Tekniska Högskolan.

Titel: Doktorandseminarium.

On approximation and estimation of some Gaussian processes with kernel representation.

Sammanfattning: We use a general representation of continuous Gaussian processes as the limit of elements in its Cameron-Martin space, to some Gaussian processes with kernel representation, $X_t = \int V(t,s)dB_s$. Examples include fractional Brownain motion. As special cases of this representation we obtain for example, the Karhunen-Loeve 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 show how to estimate the mean-reverting parameter in an Ornstein-Uhlenbeck process driven by fractional Brownian motion.

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