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Stationary distributions for diffusions with inert drift
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Bass, Richard F., Burdzy, K. (Krzysztof), Chen, ZhenQing and Hairer, Martin. (2010) Stationary distributions for diffusions with inert drift. Probability Theory and Related Fields, Vol.146 (No.12). pp. 147. ISSN 01788051
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Official URL: http://dx.doi.org/10.1007/s0044000801826
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:  01788051  
Official Date:  January 2010  
Dates: 


Volume:  Vol.146  
Number:  No.12  
Page Range:  pp. 147  
DOI:  10.1007/s0044000801826  
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:  DMS0601783 (NSF), DMS0600206 (NSF), EP/D071593 (EPSRC)  
References:  [1] R. Bass, Diffusions and Elliptic Operators. Berlin, Springer, 1997. 

URI:  http://wrap.warwick.ac.uk/id/eprint/2494 
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