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Reflected Brownian motion in a cone: Semimartingale property
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  • Published: June 1995

Reflected Brownian motion in a cone: Semimartingale property

  • Youngmee Kwon1 

Probability Theory and Related Fields volume 101, pages 211–226 (1995)Cite this article

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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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Author information

Authors and Affiliations

  1. Department of Computer Science and Statistics, Hansung University, 389 2 ga Samsun-dong Sungbuk-gu, 136-792, Seoul, Korea

    Youngmee Kwon

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  1. Youngmee Kwon
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Additional information

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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  • Received: 09 April 1993

  • Revised: 07 June 1994

  • Issue Date: June 1995

  • DOI: https://doi.org/10.1007/BF01375825

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Mathematics Subject Classification (1991)

  • 60J60
  • 60J65
  • 60G44
  • 60K25
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