The Annals of Probability

The Adjoint Process of Killed Reflected Brownian Motion in a Cone and Applications

R. Dante DeBlassie

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Abstract

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).

Article information

Source
Ann. Probab., Volume 27, Number 4 (1999), 1679-1737.

Dates
First available in Project Euclid: 31 May 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1022874812

Digital Object Identifier
doi:10.1214/aop/1022874812

Mathematical Reviews number (MathSciNet)
MR1742885

Zentralblatt MATH identifier
0965.60069

Subjects
Primary: 60J60: Diffusion processes [See also 58J65]
Secondary: 60J35: Transition functions, generators and resolvents [See also 47D03, 47D07]

Keywords
Reflected Brownian motion killed process cone radially homogeneous reection Martin boundary invariant measure

Citation

DeBlassie, R. Dante. The Adjoint Process of Killed Reflected Brownian Motion in a Cone and Applications. Ann. Probab. 27 (1999), no. 4, 1679--1737. doi:10.1214/aop/1022874812. https://projecteuclid.org/euclid.aop/1022874812


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