Small ball estimates for Brownian motion and the Brownian sheet (Q685737)
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scientific article; zbMATH DE number 423615
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Small ball estimates for Brownian motion and the Brownian sheet |
scientific article; zbMATH DE number 423615 |
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Small ball estimates for Brownian motion and the Brownian sheet (English)
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3 October 1993
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Introduce the Hölder norm \(\| f\|_ \alpha=\sup(| f(t)- f(s)|/| t-s|^ \alpha)\). The authors study the asymptotic behaviour of \(P[\| W\|_ \alpha\leq\varepsilon]\) as \(\varepsilon\to 0\), where \(W\) is the Brownian motion. The corresponding results for the Brownian sheet are also considered.
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asymptotic behaviour
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Brownian motion
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Brownian sheet
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0.9512595
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0.9488658
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0.9192592
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0.90527767
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