A note on small ball probability of a Gaussian process with stationary increments

Qi Man Shao

doi:10.1007/BF01066719

A note on small ball probability of a Gaussian process with stationary increments

Qi Man Shao^*

^*Corresponding author for this work

Research output: Contribution to journal › Journal Article › peer-review

35 Citations (Scopus)

Abstract

Let {X(t), 0≤t≤1} be a Gaussian process with mean zero and stationary increments. Let σ²(h) =EX²(h) be nondecreasing and concave on (0,1). A sharp bound on the small ball probability of X(·) is given in this paper.

Original language	English
Pages (from-to)	595-602
Number of pages	8
Journal	Journal of Theoretical Probability
Volume	6
Issue number	3
DOIs	https://doi.org/10.1007/BF01066719
Publication status	Published - Jul 1993
Externally published	Yes

Keywords

Gaussian process
Small ball probability
fractional Wiener process

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10.1007/BF01066719

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abstract = "Let \{X(t), 0≤t≤1\} be a Gaussian process with mean zero and stationary increments. Let σ2(h) =EX2(h) be nondecreasing and concave on (0,1). A sharp bound on the small ball probability of X(·) is given in this paper.",

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year = "1993",

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AB - Let {X(t), 0≤t≤1} be a Gaussian process with mean zero and stationary increments. Let σ2(h) =EX2(h) be nondecreasing and concave on (0,1). A sharp bound on the small ball probability of X(·) is given in this paper.

KW - Gaussian process

KW - Small ball probability

KW - fractional Wiener process

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U2 - 10.1007/BF01066719

DO - 10.1007/BF01066719

M3 - Journal Article

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SP - 595

EP - 602

JO - Journal of Theoretical Probability

JF - Journal of Theoretical Probability

IS - 3

ER -

A note on small ball probability of a Gaussian process with stationary increments

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Keywords

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