scholarly journals On small deviations of Gaussian processes using majorizing measures

2012 ◽  
Vol 129 (1) ◽  
pp. 41-59 ◽  
Author(s):  
Michel J. G. Weber
Keyword(s):  
Gaussian Processes ◽  
Small Deviations ◽  
Majorizing Measures

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

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.

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.

scholarly journals Small Deviations of Smooth Stationary Gaussian Processes

2009 ◽  
Vol 53 (4) ◽  
pp. 697-707 ◽  
Author(s):  
F. Aurzada ◽  
I. A. Ibragimov ◽  
M. A. Lifshits ◽  
J. H. van Zanten
Keyword(s):  
Gaussian Processes ◽  
Small Deviations ◽  
Stationary Gaussian Processes

Microstructural Evolution in Reduced TiO2

1981 ◽  
Vol 39 ◽  
pp. 74-75
Author(s):  
W. T. Donlon ◽  
S. Shinozaki ◽  
E. M. Logothetis ◽  
W. Kaizer
Keyword(s):  
Microstructural Evolution ◽  
Point Defects ◽  
Extended Defects ◽  
Small Deviations ◽  
Controlled Atmospheres ◽  
Limited Solubility ◽  
Thin Foils ◽  
Heat Treated ◽  
Porous Polycrystalline ◽  
Crystallographic Shear

Since point defects have a limited solubility in the rutile (TiO2) lattice, small deviations from stoichiometry are known to produce crystallographic shear (CS) planes which accomodate local variations in composition. The material used in this study was porous polycrystalline TiO2 (60% dense), in the form of 3mm. diameter disks, 1mm thick. Samples were mechanically polished, ion-milled by conventional techniques, and initially examined with the use of a Siemens EM102. The electron transparent thin foils were then heat-treated under controlled atmospheres of CO/CO2 and H2 and reexamined in the same manner.The “as-received” material contained mostly TiO2 grains (∼5μm diameter) which had no extended defects. Several grains however, aid exhibit a structure similar to micro-twinned grains observed in reduced rutile. Lattice fringe images (Fig. 1) of these grains reveal that the adjoining layers are not simply twin related variants of a single TinO2n-1 compound. Rather these layers (100 - 250 Å wide) are alternately comprised of stoichiometric TiO2 (rutile) and reduced TiO2 in the form of Ti8O15, with the Ti8O15 layers on either side of the TiO2 being twin related.

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