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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

8 Extrapolation of processes with periodically correlated increments observed with noise

In this chapter, we deal with the extrapolation problem for stochastic processes with periodically stationary dth increments observed with noise.

By the extrapolation problem we understand 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 ζ(t)=ξ(t)+η(t) at points t<0, where η(t) is an uncorrelated with the process ξ(t) periodically stationary stochastic process.

8.1 Hilbert space projection method of extrapolation

Let a periodically ...

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Publisher Resources

ISBN: 9783111326252