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We modify Talagrand's generic chaining method to obtain upper bounds for all p-th moments of the supremum of a stochastic process.
Convex functions and Orlicz spaces
M. Krasnosel’skiĭ and Ja. Rutickiĭ · 1961
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A bound on tail probabilities for quadratic forms in independent random variables
D. Hanson and F. Wright · 1971
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Regularity of Gaussian processes
M. Talagrand · 1987
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Probability in Banach spaces
M. Ledoux and M. Talagrand · 1991
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On decoupling, series expansions, and tail behavior of chaos processes
M. Arcones and E. Giné · 1993
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Weak convergence and empirical processes
A. van der Vaart and J. Wellner · 1996
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The concentration of measure phenomenon
M. Ledoux · 2001
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Majorizing measures without measures
M. Talagrand · 2001
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Empirical processes and random projections
B. Klartag and S. Mendelson · 2005
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The generic chaining
M. Talagrand · 2005
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Near-optimal signal recovery from random projections: universal encoding strategies?
E. Candès and T. Tao · 2006
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Reconstruction and subgaussian operators in asymptotic geometric analysis
S. Mendelson, A. Pajor, and N. Tomczak-Jaegermann · 2007
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Supremum concentration inequality and modulus of continuity for sub- n n th chaos processes
F. Viens and A. Vizcarra · 2007
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On sparse reconstruction from Fourier and Gaussian measurements
M. Rudelson and R. Vershynin · 2008
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Compressive sensing and structured random matrices
H. Rauhut · 2010
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Oracle Inequalities in Empirical Risk Minimization and Sparse Recovery Problems
V. Koltchinskii · 2011
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Weak and strong moments of random vectors
R. Latała · 2011
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Concentration Inequalities: A Nonasymptotic Theory of Independence
S. Boucheron, G. Lugosi, and P. Massart · 2013
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A Mathematical Introduction to Compressive Sensing
S. Foucart and H. Rauhut · 2013
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A tail inequality for suprema of unbounded empirical processes with applications to Markov chains
R. Adamczak · 2008
Cited alongside, same era.
Dimensionality reduction with subgaussian matrices: a unified theory
S. Dirksen
Cited in the paper.
The Bernstein–Orlicz norm and deviation inequalities
S. van de Geer and J. Lederer
Cited in the paper.
Suprema of chaos processes and the restricted isometry property
F. Krahmer, S. Mendelson, and H. Rauhut
Cited in the paper.
Hanson-Wright inequality and sub-gaussian concentration
M. Rudelson and R. Vershynin
Cited in the paper.
Upper and Lower Bounds for Stochastic Processes
M. Talagrand
Cited in the paper.