The adjoint process of killed reflected Brownian motion in a cone and applications

• 成果类型: Article
• 署名作者: DeBlassie, RD
• 署名单位: Texas A&M University System; Texas A&M University College Station
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1022874812
• 发表日期: 1999
• 页码: 1679-1737
• 关键词: boundary-conditions; uniqueness; wedge

摘要

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).