Communications in Mathematical Physics

, Volume 86, Issue 1, pp 143–147 | Cite as

Brownian motion in a convex ring and quasi-concavity

  • Christer Borell


LetX be the Brownian motion in ℝ n and denote by τ M the first hitting time ofM⫅ℝ n . Given convex setsKL⫅ℝ n 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.


Neural Network Statistical Physic Complex System Brownian Motion Nonlinear Dynamics 
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Copyright information

© Springer-Verlag 1982

Authors and Affiliations

  • Christer Borell
    • 1
  1. 1.Chalmers University of TechnologyGöteborgSweden

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