On the convex hull of symmetric stable processes

2010/04/09 by Jürgen Kampf, Kampf, Jürgen, Last, Günter · 1 citation
Mathematics · Biochemistry, Genetics and Molecular Biology · #Point processes and geometric inequalities #Diffusion and Search Dynamics #Prion Diseases and Protein Misfolding

paper · pdf · doi:10.48550/arxiv.1004.1534

Abstract

Let alpha ∈ (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 → 0.

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• Improved bounds on the inradius and inverse inradius process of the convex hull of planar Brownian motion

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