On the convex hull of symmetric stable processes

Jürgen Kampf; Günter Last

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arXiv · 1004.1534

On the convex hull of symmetric stable processes

Jürgen Kampf·Günter Last

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Abstract

Let alpha \in (1, 2] and X be an R^d-valued alpha-stable process with independent and symmetric components starting in 0. We 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 of this paper 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 \to 0.

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Jürgen Kampf, Günter Last. 2010-04-09. On the convex hull of symmetric stable processes. https://arxiv.org/abs/1004.1534

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