Summary
In this paper, the object of study is reflected Brownian motion in a cone ind-dimensions (d≧3) with nonconstant oblique reflection on each radial line emanating from the vertex of the cone. The basic question considered here is “When is this process a semimartingale?”. Conditions for the existence and uniqueness of the process for which the vertex is an instantaneous state were given by Kwon, which is resolved in terms of a real parameter α∞ depending on the cone and the direction of reflection. It is shown that starting from any point of the cone, the process is a semimartingale if α∞ < 1, α∞ + 0 and not a semimartingale if < α∞ < 2.
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This research is supported by KOSEF grant 941-0100-011-1
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Kwon, Y. Reflected Brownian motion in a cone: Semimartingale property. Probab. Th. Rel. Fields 101, 211–226 (1995). https://doi.org/10.1007/BF01375825
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DOI: https://doi.org/10.1007/BF01375825
Mathematics Subject Classification (1991)
- 60J60
- 60J65
- 60G44
- 60K25