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Stationary distributions for diffusions with inert drift

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Bass, Richard F., Burdzy, K. (Krzysztof), Chen, Zhen-Qing and Hairer, Martin. (2010) Stationary distributions for diffusions with inert drift. Probability Theory and Related Fields, Vol.146 (No.1-2). pp. 1-47. ISSN 0178-8051

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Official URL: http://dx.doi.org/10.1007/s00440-008-0182-6

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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Stochastic processes, Differential equations -- Numerical solutions, Markov processes -- Numerical solutions, Diffusion processes
Journal or Publication Title:	Probability Theory and Related Fields
Publisher:	Springer
ISSN:	0178-8051
Date:	January 2010
Volume:	Vol.146
Number:	No.1-2
Page Range:	pp. 1-47
Identification Number:	10.1007/s00440-008-0182-6
Status:	Peer Reviewed
Access rights to Published version:	Open Access
Funder:	Engineering and Physical Sciences Research Council (EPSRC), National Science Foundation (U.S.) (NSF)
Grant number:	DMS-0601783 (NSF), DMS-0600206 (NSF), EP/D071593 (EPSRC)
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URI:	http://wrap.warwick.ac.uk/id/eprint/2494