Stationary distributions for diffusions with inert drift

Richard F. Bass; Krzysztof Burdzy; Zhen Qing Chen; Martin Hairer

doi:10.1007/s00440-008-0182-6

Stationary distributions for diffusions with inert drift

Richard F. Bass, Krzysztof Burdzy^*, Zhen Qing Chen, Martin Hairer

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

14 Citations (Scopus)

Abstract

Consider reflecting Brownian motion in a bounded domain in 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.

Original language	English
Pages (from-to)	1-47
Number of pages	47
Journal	Probability Theory and Related Fields
Volume	146
Issue number	1
DOIs	https://doi.org/10.1007/s00440-008-0182-6
Publication status	Published - Oct 2009
Externally published	Yes

Keywords

60J60
Primary: 60H10
Secondary: 60J55

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10.1007/s00440-008-0182-6

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Bass, R. F., Burdzy, K., Chen, Z. Q., & Hairer, M. (2009). Stationary distributions for diffusions with inert drift. Probability Theory and Related Fields, 146(1), 1-47. https://doi.org/10.1007/s00440-008-0182-6

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AU - Burdzy, Krzysztof

AU - Chen, Zhen Qing

AU - Hairer, Martin

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N2 - Consider reflecting Brownian motion in a bounded domain in ℝd 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.

AB - Consider reflecting Brownian motion in a bounded domain in ℝd 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.

KW - 60J60

KW - Primary: 60H10

KW - Secondary: 60J55

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SP - 1

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JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1

ER -

Stationary distributions for diffusions with inert drift

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