An Introduction to the Theory of Stationary Random Functions

Yaglom, A. M.; Newell, G. F.

doi:10.1115/1.3636602

Cited by 239 publications

(282 citation statements)

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“…As a result, certain measures including power spectrum and autocorrelation function (ACF) [7,8] are associated with significant errors and their use is questionable [9]. The term stationarity/non-stationarity refers to the underlying process, not to a particular realisation of it.…”

Section: Introductionmentioning

confidence: 99%

Characterisation of linear predictability and non-stationarity of subcutaneous glucose profiles

Khovanova

Khovanov

Sbano

et al. 2013

Computer Methods and Programs in Biomedicine

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Abstract-Continuous glucose monitoring is increasingly used in the management of diabetes.Subcutaneous glucose profiles are characterized by a strong non-stationarity, which limits the application of correlation-spectral analysis. We derived an index of linear predictability by calculating the autocorrelation function of time series increments and applied detrended fluctuation analysis to assess the non-stationarity of the profiles. Time series from volunteers with both type 1 and type 2 diabetes and from control subjects were analysed. The results suggest that in control subjects, blood glucose variation is relatively uncorrelated, and this variation could be modelled as a random walk with no retention of 'memory' of previous values.In diabetes, variation is both greater and smoother, with retention of inter-dependence between neighboring values. Essential components for adequate longer term prediction were identified via a decomposition of time series into a slow trend and responses to external stimuli. Implications for diabetes management are discussed.

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Section: Introductionmentioning

confidence: 99%

Characterisation of linear predictability and non-stationarity of subcutaneous glucose profiles

Khovanova

Khovanov

Sbano

et al. 2013

Computer Methods and Programs in Biomedicine

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“…A classical criterion of Szego shows that the term (iii) of Theorem 2.2 (h) is zero. The prediction problem may be solved by "Yaglom's method" and yields [17]. (6.6S) From this it is again straightforward, but somewhat tedious, to compute our…”

Section: J -Oomentioning

confidence: 99%

A post-predictive view of gaussian processes

Knight¹

1983

Ann. Sci. École Norm. Sup.

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“…(2.6) (See a discussion concerning this result in [40] and the references therein.) On can also deduce from this result an integral representation for Gaussian fields with stationary increments.…”

Section: R(t S) =mentioning

confidence: 99%

Stationary Gaussian random fields on hyperbolic spaces and on Euclidean spheres

Cohen¹,

Lifshits²

2012

ESAIM: PS

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Abstract.We recall necessary notions about the geometry and harmonic analysis on a hyperbolic space and provide lecture notes about homogeneous random functions parameterized by this space. The general principles are illustrated by construction of numerous examples analogous to Euclidean case. We also give a brief survey of the fields parameterized by Euclidean spheres. At the end we give a list of important open questions in hyperbolic case.Mathematics Subject Classification. 60G15, 60G10, 51M10.

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An Introduction to the Theory of Stationary Random Functions

Cited by 239 publications

References 0 publications

Characterisation of linear predictability and non-stationarity of subcutaneous glucose profiles

Characterisation of linear predictability and non-stationarity of subcutaneous glucose profiles

A post-predictive view of gaussian processes

Stationary Gaussian random fields on hyperbolic spaces and on Euclidean spheres

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