scholarly journals Degenerate self-similar measures, spectral asymptotics and small deviations of Gaussian processes

2011 ◽  
Vol 44 (1) ◽  
pp. 12-24 ◽  
Author(s):  
A. I. Nazarov ◽  
I. A. Sheipak
Keyword(s):  
Gaussian Processes ◽  
Spectral Asymptotics ◽  
Small Deviations ◽  
Self Similar

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 Symmetric Stochastic Integrals with Respect to a Class of Self-similar Gaussian Processes

2018 ◽  
Vol 32 (3) ◽  
pp. 1105-1144
Author(s):  
Daniel Harnett ◽  
Arturo Jaramillo ◽  
David Nualart
Keyword(s):  
Gaussian Processes ◽  
Stochastic Integrals ◽  
Self Similar

On the Lamperti transform of the fractional Brownian sheet

2016 ◽  
Vol 19 (6) ◽  
Author(s):  
Marwa Khalil ◽  
Ciprian Tudor ◽  
Mounir Zili
Keyword(s):  
Differential Equation ◽  
Brownian Motion ◽  
Stochastic Differential Equation ◽  
Gaussian Processes ◽  
Stationary Process ◽  
Similar Process ◽  
Brownian Sheet ◽  
Fractional Brownian Sheet ◽  
Self Similar ◽  
Strictly Stationary Process

AbstractIn 1962 Lamperti introduced a transformation that associates to every non-trivial self-similar process a strictly stationary process. This transform has been widely studied for Gaussian processes and in particular for fractional Brownian motion. Our aim is to analyze various properties of the Lamperti transform of the fractional Brownian sheet. We give the stochastic differential equation satisfied by this transform and we represent it as a series of independent Ornstein-Uhlenbeck sheets.

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