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Stationary distributions for diffusions with inert drift
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  • Published: 04 November 2008

Stationary distributions for diffusions with inert drift

  • Richard F. Bass1,
  • Krzysztof Burdzy2,
  • Zhen-Qing Chen2 &
  • …
  • Martin Hairer3 

Probability Theory and Related Fields volume 146, Article number: 1 (2010) Cite this article

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  • 14 Citations

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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.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Connecticut, Storrs, CT, 06269-3009, USA

    Richard F. Bass

  2. Department of Mathematics, University of Washington, Seattle, WA, 98195, USA

    Krzysztof Burdzy & Zhen-Qing Chen

  3. Mathematics Institute, The University of Warwick, Coventry, CV4 7AL, UK

    Martin Hairer

Authors
  1. Richard F. Bass
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  2. Krzysztof Burdzy
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  3. Zhen-Qing Chen
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  4. Martin Hairer
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Corresponding author

Correspondence to Krzysztof Burdzy.

Additional information

Research supported in part by NSF Grants DMS-0601783 and DMS-0600206 and by EPSRC Grant EP/D071593/.

K. Burdzy and M. Hairer gratefully acknowledge the hospitality and support of the Institut Mittag-Leffler, where part of this research was done.

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Bass, R.F., Burdzy, K., Chen, ZQ. et al. Stationary distributions for diffusions with inert drift. Probab. Theory Relat. Fields 146, 1 (2010). https://doi.org/10.1007/s00440-008-0182-6

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  • Received: 25 April 2008

  • Revised: 05 October 2008

  • Published: 04 November 2008

  • DOI: https://doi.org/10.1007/s00440-008-0182-6

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Mathematics Subject Classification (2000)

  • Primary: 60H10
  • Secondary: 60J55
  • 60J60
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