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Some extensions of linear approximation and prediction problems for stationary processes. / Ibragimov, Ildar; Kabluchko, Zakhar; Lifshits, Mikhail.

In: Stochastic Processes and their Applications, Vol. 129, No. 8, 01.08.2019, p. 2758-2782.

Research output: Contribution to journal › Article › peer-review

Harvard

Ibragimov, I, Kabluchko, Z & Lifshits, M 2019, 'Some extensions of linear approximation and prediction problems for stationary processes', Stochastic Processes and their Applications, vol. 129, no. 8, pp. 2758-2782. https://doi.org/10.1016/j.spa.2018.08.001

APA

Ibragimov, I., Kabluchko, Z., & Lifshits, M. (2019). Some extensions of linear approximation and prediction problems for stationary processes. Stochastic Processes and their Applications, 129(8), 2758-2782. https://doi.org/10.1016/j.spa.2018.08.001

Vancouver

Ibragimov I, Kabluchko Z, Lifshits M. Some extensions of linear approximation and prediction problems for stationary processes. Stochastic Processes and their Applications. 2019 Aug 1;129(8):2758-2782. https://doi.org/10.1016/j.spa.2018.08.001

Author

Ibragimov, Ildar ; Kabluchko, Zakhar ; Lifshits, Mikhail. / Some extensions of linear approximation and prediction problems for stationary processes. In: Stochastic Processes and their Applications. 2019 ; Vol. 129, No. 8. pp. 2758-2782.

BibTeX

@article{e9608dd013954d32b5ea0b4fe17539bf,
title = "Some extensions of linear approximation and prediction problems for stationary processes",
abstract = "Let (B(t)) t∈Θ with Θ=Z or Θ=R be a wide sense stationary process with discrete or continuous time. The classical linear prediction problem consists of finding an element in span¯{B(s),s≤t} providing the best possible mean square approximation to the variable B(τ) with τ>t. In this article we investigate this and some other similar problems where, in addition to prediction quality, optimization takes into account other features of the objects we search for. One of the most motivating examples of this kind is an approximation of a stationary process B by a stationary differentiable process X taking into account the kinetic energy that X spends in its approximation efforts. ",
keywords = "стационарные процессы, аппроксимация, ПРОГНОЗИРОВАНИЕ, Energy saving approximation, Interpolation, Prediction, Wide sense stationary process",
author = "Ildar Ibragimov and Zakhar Kabluchko and Mikhail Lifshits",
year = "2019",
month = aug,
day = "1",
doi = "10.1016/j.spa.2018.08.001",
language = "English",
volume = "129",
pages = "2758--2782",
journal = "Stochastic Processes and their Applications",
issn = "0304-4149",
publisher = "Elsevier",
number = "8",

}

RIS

TY - JOUR

T1 - Some extensions of linear approximation and prediction problems for stationary processes

AU - Ibragimov, Ildar

AU - Kabluchko, Zakhar

AU - Lifshits, Mikhail

PY - 2019/8/1

Y1 - 2019/8/1

N2 - Let (B(t)) t∈Θ with Θ=Z or Θ=R be a wide sense stationary process with discrete or continuous time. The classical linear prediction problem consists of finding an element in span¯{B(s),s≤t} providing the best possible mean square approximation to the variable B(τ) with τ>t. In this article we investigate this and some other similar problems where, in addition to prediction quality, optimization takes into account other features of the objects we search for. One of the most motivating examples of this kind is an approximation of a stationary process B by a stationary differentiable process X taking into account the kinetic energy that X spends in its approximation efforts.

AB - Let (B(t)) t∈Θ with Θ=Z or Θ=R be a wide sense stationary process with discrete or continuous time. The classical linear prediction problem consists of finding an element in span¯{B(s),s≤t} providing the best possible mean square approximation to the variable B(τ) with τ>t. In this article we investigate this and some other similar problems where, in addition to prediction quality, optimization takes into account other features of the objects we search for. One of the most motivating examples of this kind is an approximation of a stationary process B by a stationary differentiable process X taking into account the kinetic energy that X spends in its approximation efforts.

KW - стационарные процессы

KW - аппроксимация

KW - ПРОГНОЗИРОВАНИЕ

KW - Energy saving approximation

KW - Interpolation

KW - Prediction

KW - Wide sense stationary process

UR - https://www.sciencedirect.com/science/article/abs/pii/S0304414918304046

UR - http://www.scopus.com/inward/record.url?scp=85054141013&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/some-extensions-linear-approximation-prediction-problems-stationary-processes

U2 - 10.1016/j.spa.2018.08.001

DO - 10.1016/j.spa.2018.08.001

M3 - Article

VL - 129

SP - 2758

EP - 2782

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

SN - 0304-4149

IS - 8

ER -

ID: 35792719