1 Citation (Scopus)

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.

Translated title of the contributionНекоторые обобщения задач линейной аппроксимации и прогнозирования стационарных процессов
Original languageEnglish
Pages (from-to)2758-2782
Number of pages25
JournalStochastic Processes and their Applications
Volume129
Issue number8
DOIs
Publication statusPublished - 1 Aug 2019

Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Statistics and Probability
  • Modelling and Simulation

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