Comparison theorems for small deviations of random series
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Publication:1767504
zbMath1065.60040MaRDI QIDQ1767504
Fuchang Gao, Fred Torcaso, Jan Hannig
Publication date: 8 March 2005
Published in: Electronic Journal of Probability (Search for Journal in Brave)
Full work available at URL: https://eudml.org/doc/124791
Gaussian processes (60G15) Inequalities; stochastic orderings (60E15) Sums of independent random variables; random walks (60G50) Large deviations (60F10)
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Comparison theorems for the small ball probabilities of the Green Gaussian processes in weighted $L_2$-norms ⋮ Comparison for upper tail probabilities of random series ⋮ Precise small deviations in \(L_2\) of some Gaussian processes appearing in the regression context ⋮ \( L_2\)-small ball asymptotics for Gaussian random functions: a survey ⋮ \(L_2\)-small ball asymptotics for a family of finite-dimensional perturbations of Gaussian functions ⋮ Exact \(L_2\)-small ball asymptotics for some Durbin processes ⋮ Exact asymptotics of small deviations for a stationary Ornstein-Uhlenbeck process and some Gaussian diffusion processes in the L p -norm, 2 ≤ p ≤ ∞ ⋮ Nonparametric estimation of infinite order regression and its application to the risk-return tradeoff ⋮ Logarithmic level comparison for small deviation probabilities ⋮ Spectral asymptotics for problems with integral constraints ⋮ Logarithmic level comparison for small deviation probabilities ⋮ A short note on small deviations of sequences of i.i.d. random variables with exponentially decreasing weights ⋮ On the lower tail probabilities of some random sequences in \(l_{ p }\) ⋮ The Small Ball Asymptotics in Hilbert Norm for the Kac--Kiefer--Wolfowitz Processes ⋮ Estimation of functional derivatives ⋮ Spectral asymptotics for a class of integro-differential equations arising in the theory of fractional Gaussian processes
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