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Brownian motion in a convex ring and quasi-concavity

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Abstract

LetX be the Brownian motion in ℝn and denote by τ M the first hitting time ofM⫅ℝn. Given convex setsK⫅L⫅ℝn we prove that all the level sets

$$\{ \left( {x,t} \right) \in \mathbb{R}^n \times [0, + \infty [;P_x [\tau _K \leqq t \wedge \tau _{L^c } ] \geqq \lambda \} ,\lambda \in \mathbb{R}$$

are convex.

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Authors and Affiliations

  1. Chalmers University of Technology, S-41296, Göteborg, Sweden

    Christer Borell

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  1. Christer Borell
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Communicated by B. Simon

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Borell, C. Brownian motion in a convex ring and quasi-concavity. Commun.Math. Phys. 86, 143–147 (1982). https://doi.org/10.1007/BF01205665

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  • DOI: https://doi.org/10.1007/BF01205665

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