On the convex hull of symmetric stable processes (Q2845067)
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scientific article; zbMATH DE number 6200429
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the convex hull of symmetric stable processes |
scientific article; zbMATH DE number 6200429 |
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On the convex hull of symmetric stable processes (English)
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22 August 2013
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convex hull
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symmetric stable process
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0.91580755
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0.9130519
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0.90996516
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0.9011996
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The object of this paper is an \(\mathbb R^d\)-valued symmetric \(\alpha\)-stable Lévy process starting at the origin. The authors consider the closure \(S_t\) of the path described by \(X\) on the interval \([0, t]\) and its convex hull \(Z_t\). The first result provides a formula for certain mean mixed volumes of \(Z_t\), and in particular for the expected first intrinsic volume of \(Z_t\). The second result deals with the asymptotics of the expected volume of the stable sausage \(Z_t+B\) (where \(B\) is an arbitrary convex body with interior points) as \(t\to0\). For this, the authors assume that \(X\) has independent components.
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