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Stationary distributions for diffusions with inert drift

  • Richard F. Bass
  • Krzysztof Burdzy
  • Zhen-Qing Chen
  • Martin Hairer
Article

Abstract

Consider reflecting Brownian motion in a bounded domain in \({\mathbb R^d}\) that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting Brownian motion and the value of the drift vector has a product form. Moreover, the first component is uniformly distributed on the domain, and the second component has a Gaussian distribution. We also consider more general reflecting diffusions with inert drift as well as processes where the drift is given in terms of the gradient of a potential.

Mathematics Subject Classification (2000)

Primary: 60H10 Secondary: 60J55 60J60 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Richard F. Bass
    • 1
  • Krzysztof Burdzy
    • 2
  • Zhen-Qing Chen
    • 2
  • Martin Hairer
    • 3
  1. 1.Department of MathematicsUniversity of ConnecticutStorrsUSA
  2. 2.Department of MathematicsUniversity of WashingtonSeattleUSA
  3. 3.Mathematics InstituteThe University of WarwickCoventryUK

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