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January 2004 Lower tail probabilities for Gaussian processes
Wenbo V. Li, Qi-Man Shao
Ann. Probab. 32(1A): 216-242 (January 2004). DOI: 10.1214/aop/1078415834

Abstract

Let $X=(X_t)_{t \in S}$ be a real-valued Gaussian random process indexed by S with mean zero. General upper and lower estimates are given for the lower tail probability $\mathbb{P}(\sup_{t \in S} (X_t-X_{t_0}) \leq x )$ as $x \to 0$, with $t_0\in S$ fixed. In particular, sharp rates are given for fractional Brownian sheet. Furthermore, connections between lower tail probabilities for Gaussian processes with stationary increments and level crossing probabilities for stationary Gaussian processes are studied. Our methods also provide useful information on a random pursuit problem for fractional Brownian particles.

Citation

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Wenbo V. Li. Qi-Man Shao. "Lower tail probabilities for Gaussian processes." Ann. Probab. 32 (1A) 216 - 242, January 2004. https://doi.org/10.1214/aop/1078415834

Information

Published: January 2004
First available in Project Euclid: 4 March 2004

zbMATH: 1052.60028
MathSciNet: MR2040781
Digital Object Identifier: 10.1214/aop/1078415834

Subjects:
Primary: 60G15
Secondary: 60G17, 60G60

Rights: Copyright © 2004 Institute of Mathematical Statistics

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Vol.32 • No. 1A • January 2004
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