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Communications in Mathematical Physics

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

Brownian motion in a convex ring and quasi-concavity

  • Christer Borell
Article

Abstract

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.

Keywords

Neural Network Statistical Physic Complex System Brownian Motion Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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