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

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.

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