On an extremal problem in Hp and prediction of p-stable processes 0
(1994) In Stochastic analysis on infinite dimensional spaces: proceedings of the U.S.-Japan bilateral seminar, January 4-8 1994, Baton Rouge, Louisiana 310. p.1-11- Abstract
- 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1467472
- author
- Aleman, Alexandru ^{LU} ; Rajput, Balram and Richter, Stefan
- publishing date
- 1994
- type
- Chapter in Book/Report/Conference proceeding
- publication status
- published
- subject
- in
- Stochastic analysis on infinite dimensional spaces: proceedings of the U.S.-Japan bilateral seminar, January 4-8 1994, Baton Rouge, Louisiana
- volume
- 310
- pages
- 1 - 11
- publisher
- Pitman research notes in mathematics series
- ISBN
- 978-0-582-24490-0
- language
- English
- LU publication?
- no
- id
- 51b65368-b363-401a-8d67-dad911bf1ddb (old id 1467472)
- date added to LUP
- 2009-09-16 14:42:49
- date last changed
- 2018-05-29 12:16:48
@inbook{51b65368-b363-401a-8d67-dad911bf1ddb, abstract = {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 = {Aleman, Alexandru and Rajput, Balram and Richter, Stefan}, isbn = {978-0-582-24490-0}, language = {eng}, pages = {1--11}, publisher = {Pitman research notes in mathematics series}, series = {Stochastic analysis on infinite dimensional spaces: proceedings of the U.S.-Japan bilateral seminar, January 4-8 1994, Baton Rouge, Louisiana}, title = {On an extremal problem in Hp and prediction of p-stable processes 0}, volume = {310}, year = {1994}, }