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

Aleman, Alexandru LU ; Rajput, Balram and Richter, Stefan (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)
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author
publishing date
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
2016-06-29 09:19:04
@misc{51b65368-b363-401a-8d67-dad911bf1ddb,
  abstract     = {This paper provides new and interesting features on an extremal problem in the space of Hardy functions, $H^p, \; 0&lt;p&lt;1$, 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 $p, \; 0&lt;p&lt;1$. 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    = {ARRAY(0x88a7060)},
  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},
}