scholarly journals On Small Deviation Asymptotics in the L2-Norm for Certain Gaussian Processes

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 655
Author(s):  
Leonid Rozovsky
Keyword(s):  
Gaussian Processes ◽  
Special Form ◽  
Small Deviation ◽  
Small Deviations ◽  
L2 Norm ◽  
Hilbert Norm

The results obtained allow finding sharp small deviations in a Hilbert norm for centered Gaussian processes in the case where their covariances have a special form of the eigenvalues and allow us to describe small deviation asymptotics for certain Gaussian processes.

Precise small deviations in L 2 of some Gaussian processes appearing in the regression context

2014 ◽  
Vol 12 (11) ◽  
Author(s):  
Alisa Kirichenko ◽  
Ya. Nikitin
Keyword(s):  
Brownian Motion ◽  
Gaussian Processes ◽  
Small Deviation ◽  
Small Deviations ◽  
Hilbert Norm

AbstractWe find precise small deviation asymptotics with respect to the Hilbert norm for some special Gaussian processes connected to two regression schemes studied by MacNeill and his coauthors. In addition, we also obtain precise small deviation asymptotics for the detrended Brownian motion and detrended Slepian process.

Detailed finer features in spectra of interfacial waves for characterization of a bubble-laden drop

2017 ◽  
Vol 831 ◽  
pp. 698-718 ◽  
Author(s):  
Udugama R. Sumanasekara ◽  
Sukalyan Bhattacharya
Keyword(s):  
Small Deviation ◽  
Energy Levels ◽  
Bond Number ◽  
Small Deviations ◽  
Quantum Numbers ◽  
Novel Approach ◽  
Arbitrary Location ◽  
The Individual ◽  
Concentric Geometry

This article describes unexplored details of the intriguing spectral manifestation of the small-amplitude waves at the surfaces of a bubble-laden drop. Its natural frequencies of interfacial pulsation reveal a non-trivial variation with the position of the cavity inside the liquid. This configurational dependence of spectra is calculated for arbitrary location of the void by using a novel approach under low capillary number and low Bond number limits. The analysis is based on expansion in two sets of basis functions where their mutual transformations are utilized to enforce interfacial boundary conditions. The obtained results quantify a few important features which have both scientific and technological significance. For a concentric geometry, the inherent azimuthal degeneracy makes the frequencies for a number of vibrational modes exactly the same. For an eccentric position of the bubble, however, this degeneracy disappears, creating small deviations in the spectral values corresponding to different azimuthal modes. Such behaviour is akin to fine-structure split in an atomic system, where different quantum numbers ensure small deviation in energy levels of the states. The formulated mathematical procedure can determine the individual frequency values for the interfacial oscillation even if these are grouped closely together in bands. The paper shows how the number of fine structures inside a band and their specific values can be exploited to predict the size and position of the cavity in an opaque drop without any direct visualization of its interior.

scholarly journals Small Deviations for a Family of Smooth Gaussian Processes

2011 ◽  
Vol 26 (1) ◽  
pp. 153-168 ◽  
Author(s):  
Frank Aurzada ◽  
Fuchang Gao ◽  
Thomas Kühn ◽  
Wenbo V. Li ◽  
Qi-Man Shao
Keyword(s):  
Gaussian Processes ◽  
Small Deviations

scholarly journals On the properties of the classifier in case of small deviations of blood parameters from the norm

2021 ◽  
pp. 1-26
Author(s):  
Boris Mikhailovich Gavrikov ◽  
Mikhail Borisovich Gavrikov ◽  
Nadezhda Vladimirovna Pesryakova
Keyword(s):  
Mathematical Model ◽  
Human Health ◽  
Peripheral Blood ◽  
Polynomial Regression ◽  
Numerical Study ◽  
Small Deviation ◽  
Blood Parameters ◽  
Statistical Classification ◽  
Small Deviations ◽  
Regression Approach

A mathematical model is described and implemented, intended for the numerical study of the ability of the statistical classification method to interpolate and extrapolate. The classifier developed by the authors is based on the polynomial-regression approach and has probabilistic estimates. It is used to assess the state of human health based on the parameters of laboratory analysis of peripheral blood. The blood base is considered with a small deviation from the norm.

scholarly journals On Small Deviation Asymptotics In L2 of Some Mixed Gaussian Processes

Mathematics ◽  
2018 ◽  
Vol 6 (4) ◽  
pp. 55 ◽  
Author(s):  
Alexander Nazarov ◽  
Yakov Nikitin
Keyword(s):  
Gaussian Processes ◽  
Small Deviation
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