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October 1999 The Adjoint Process of Killed Reflected Brownian Motion in a Cone and Applications
R. Dante DeBlassie
Ann. Probab. 27(4): 1679-1737 (October 1999). DOI: 10.1214/aop/1022874812


Let $X_t$ be reflected Brownian motion (RBM) in a cone with radially homogeneous reflection, killed upon reaching the vertex of the cone. We determine the adjoint process and use it to find the Martin boundary of the killed RBM together with all the corresponding positive harmonic functions. Then we can identify and prove uniqueness (up to positive scalar multiples) of the invariant measure for killed RBM and RBM without killing. Along the way, we prove the strong Feller property of the resolvent of RBM (no killing).


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R. Dante DeBlassie. "The Adjoint Process of Killed Reflected Brownian Motion in a Cone and Applications." Ann. Probab. 27 (4) 1679 - 1737, October 1999.


Published: October 1999
First available in Project Euclid: 31 May 2002

zbMATH: 0965.60069
MathSciNet: MR1742885
Digital Object Identifier: 10.1214/aop/1022874812

Primary: 60J60
Secondary: 60J35

Keywords: cone , invariant measure , killed process , Martin boundary , radially homogeneous reection , reflected Brownian motion

Rights: Copyright © 1999 Institute of Mathematical Statistics


Vol.27 • No. 4 • October 1999
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