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Gaussian processes: Inequalities, small ball probabilities and applications

Handbook of Statistics, 2001
Publisher Summary This chapter focuses on the inequalities, small ball probabilities, and application of Gaussian processes. It is well-known that the large deviation result plays a fundamental role in studying the upper limits of Gaussian processes, such as the Strassen type law of the iterated logarithm.
Shao, Qi-Man, Li, W.V.
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Some small ball probabilities for Gaussian processes under nonuniform norms

Journal of Theoretical Probability, 1996
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Small Ball Probabilities for a Shifted Poisson Process

Journal of Mathematical Sciences, 2003
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Deheuvels, P., Lifshits, M. A.
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Small Ball Probabilities for Certain Gaussian Random Fields

Journal of Theoretical Probability, 2017
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About the Complexity Function in Small-ball Probability Factorization

2020
The Small-Ball Probability (SmBP) of a process valued in a semi-metric space is considered. Assume that it factorizes in two terms that play the role of a surrogate density and of a volumetric term, respectively. This work presents some recent developments concerning the study of the volumetric term that detains information about the complexity of the ...
enea bongiorno, aldo goia, philippe vieu
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Small ball probabilities for integrals of weighted Brownian motion

Statistics & Probability Letters, 2000
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Dunker, T., Li, W. V., Linde, W.
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Small Ball Probabilities of Fractional Brownian Sheets via Fractional Integration Operators

Journal of Theoretical Probability, 2002
The authors investigate the small ball problem for \(d\)-dimensional fractional Brownian sheets by functional analysis methods. For this reason they show that integration operators of Riemann-Liouville and Weyl type are very close in the sense of their approximation properties, i.e.
Belinsky, Eduard, Linde, Werner
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Phase retrieval without small-ball probability assumptions: Stability and uniqueness

2015 International Conference on Sampling Theory and Applications (SampTA), 2015
We study stability and uniqueness for the phase retrieval problem. That is, we ask when is a signal x e Rn stably and uniquely determined (up to small perturbations), when one performs phaseless measurements of the form y i = |aT i x|2 (for i = 1,…, N), where the vectors a i e Rn are chosen independently at random, with each coordinate a ij e R ...
Felix Krahmer, Yi-Kai Liu
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Phase retrieval without small-ball probability assumptions: Recovery guarantees for phaselift

2015 International Conference on Sampling Theory and Applications (SampTA), 2015
We study the problem of recovering an unknown vector x e Rn from measurements of the form y i = |aT i x|2 (for i = 1,…, m), where the vectors a i e Rn are chosen independently at random, with each coordinate a ij e R being chosen independently from a fixed sub-Gaussian distribution D.
Felix Krahmer, Yi-Kai Liu
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Estimates for the Small Ball Probabilities of the Fractional Brownian Sheet

Journal of Theoretical Probability, 2000
Given a stochastic process \(X=(X(t))_{t\in T}\) over an index set \(T\) which is a.s.~bounded, the small ball problem for \(X\) (in the log-level) is to determine the behaviour of \(-\log(\sup_{t\in T}|X(t)|
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