THE SUBMARTINGALE PROBLEM FOR BROWNIAN-MOTION IN A CONE WITH NONCONSTANT OBLIQUE REFLECTION

• 成果类型: Article
• 署名作者: KWON, Y
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/BF01300561
• 发表日期: 1992
• 页码: 351-391
• 关键词: boundary

摘要

This work is concerned with the existence and uniqueness of a strong Markov process that has continuous sample paths and the following additional properties. 1. The state space is a cone in d-dimensions (d greater-than-or-equal-to 3), and the process behaves in the interior of the cone like ordinary Brownian motion. 2. The process reflects instantaneously at the boundary of the cone, the direction of reflection is continuous except at the vertex and has a limit which is fixed on each radial line emanating from the vertex. 3. The amount of time that the process spends at the vertex of the cone is zero (i.e., the set of times for which the process is at the vertex has zero Lebesgue measure.)