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Non-Stationary Stochastic Processes Estimation
book

Non-Stationary Stochastic Processes Estimation

by Maksym Luz, Mikhail Moklyachuk
May 2024
Intermediate to advanced content levelIntermediate to advanced
310 pages
7h 41m
English
De Gruyter
Content preview from Non-Stationary Stochastic Processes Estimation

7 Extrapolation of processes with periodically correlated increments

In this chapter, we deal with the extrapolation problem for stochastic processes with periodically correlated dth increments. More precisely, we consider the problem of the mean square optimal linear estimation of the functionals

Aξ=0a(t)ξ(t)dt,ANTξ=0(N+1)Ta(t)ξ(t)dt,

which depend on the unknown values of a stochastic process ξ(t) with periodically correlated dth increments. Estimates are based on observations of the process ξ(t) at points t<0.

7.1 Generated stationary increment sequence representation of the functional Aξ

Lemma 7.1.1 (Luz and Moklyachuk [115]).

Any linear functional

Aξ=0a(t)ξ(t)dt

allows a representation

Aξ=BξVξ,

where

Bξ=0bτ(t
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Publisher Resources

ISBN: 9783111326252