14 Result(s)
within
**n V. Li
English
Probability Theory and Stochastic Processes
Statistics, general
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Article
Comparison results for the lower tail of Gaussian seminorms
Let ξ=(ξ n ) be i.i.d.N(0, 1) random variables andq(x), q′(x):R ∞→[0, ∞) be seminorms. We investigate necessary and sufficient conditions that the ratio ofP(q(ξ)<ε) andP(q′(ξ)<ε)...
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Article
Small ball estimates for Brownian motion and the Brownian sheet
Small ball estimates are obtained for Brownian motion and the Brownian sheet when balls are given by certain Hölder norms. As an application of these results we include a functional form of Chung's LIL in this...
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Article
Small ball probabilities for Gaussian processes with stationary increments under Hölder norms
Small ball probabilities are estimated for Gaussian processes with stationary increments when the small balls are given by various Hölder norms. As an application we establish results related to Chung's functi...
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Article
Small Ball Estimates for Gaussian Processes under Sobolev Type Norms
A sharp small ball estimate under Sobolev type norms is obtained for certain Gaussian processes in general and for fractional Brownian motions in particular. New method using the techniques in large deviation ...
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Article
Small Deviations for Gaussian Markov Processes Under the Sup-Norm
Let {X(t); 0≤t≤1} be a real-valued continuous Gaussian Markov process with mean zero and covariance σ(s, t) = EX(s) X(t) ≠ 0 for 0<s, t<1. It is known that we can write σ(s, t) = G(min(s, t)) H(max(s, t)) with G>...
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Article
A Functional LIL and Some Weighted Occupation Measure Results for Fractional Brownian Motion
Weighted occupation measure results are obtained for fractional Brownian motion. Proofs depend on small ball probability estimates of the sup-norm for these processes, which are then used to obtain a functiona...
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Chapter and Conference Paper
Small Deviation Estimates for Some Additive Processes
We study the small deviation probabilities for real valued additive processes. This naturally leads to the small deviation for the corresponding range process. Our general results can be applied to a wide rang...
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Article
Small Deviations of Stable Processes via Metric Entropy
Let X=(X(t)) t∈T be a symmetric α-stable, 0<α<2, process with paths in the dual E * of a certain Banach space E. Then there exists a (bounded, linear) operator u from E into some L α ...
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Article
Logarithmic Level Comparison for Small Deviation Probabilities
Log-level comparisons of the small deviation probabilities are studied in three different but related settings: Gaussian processes under the L 2 norm, multiple sums motivated by tensor product of ...
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Article
Logarithmic Level Comparison for Small Deviation Probabilities
Log-level comparisons of the small deviation probabilities are studied in three different but related settings: Gaussian processes under the L2 norm, multiple sums motivated by tensor product of Gaussian processe...
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Article
Logarithmic Level Comparison for Small Deviation Probabilities
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Article
A Gaussian Inequality for Expected Absolute Products
We prove the inequality that \({\mathbb{E}}|X_{1}X_{2}\cdots X_{n}|\leq \sqrt{\mathrm{per}(\varSigma )}\) , for any cent...
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Article
Small Deviations for a Family of Smooth Gaussian Processes
We study the small deviation probabilities of a family of very smooth self-similar Gaussian processes. The canonical process from the family has the same scaling property as standard Brownian motion and plays ...
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Article
A Note on Distribution-Free Symmetrization Inequalities
Let \(X, Y\) X , ...
