On an extremal problem in Hp and prediction of p-stable processes 0

Summary, in English

This paper provides new and interesting features on an extremal problem in the space of Hardy functions, $H^p, \; 0<p<1$, and then proceeds to give exact recipe formulas for extrapolating one or two steps ahead of current observations from a discrete-parameter stable harmonizable stochastic process of index $p, \; 0<p<1$. The existence of a best approximation $\tilde\phi _N$ of $z^{-N}\phi $ in $H^p$ for $\phi \in H^p$ together with an expression for $\phi (z)-z^N{\tilde{\phi}_N(z)}$ is given. It is observed that best approximation is not unique in this case, in contrast to the case $1\leq p$. For $N=1,2$, the authors provide explicit formulas for the best approximation and consequently for the best linear extrapolators. The paper lacks a working example.

• Author: Alexandru Aleman; Balram Rajput; Stefan Richter
• Publishing year: 1994
• Language: English
• Pages: 1-11
• Publication/Series: Stochastic analysis on infinite dimensional spaces: proceedings of the U.S.-Japan bilateral seminar, January 4-8 1994, Baton Rouge, Louisiana
• Volume: 310
• Document type: Book chapter
• Publisher: Pitman research notes in mathematics series
• Topic: Mathematics
• Status: Published
• ISBN/ISSN/Other: ISBN: 978-0-582-24490-0