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The submartingal problem for Brownian motion in a cone with non-constant oblique reflection
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  • Published: September 1992

The submartingal problem for Brownian motion in a cone with non-constant oblique reflection

  • Youngmee Kwon1 

Probability Theory and Related Fields volume 92, pages 351–391 (1992)Cite this article

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  • 7 Citations

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Summary

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. 1.

    The state space is a cone ind-dimensions (d≧3), and the process behaves in the interior of the cone like ordinary Brownian motion.

  2. 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. 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.)

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Author information

Authors and Affiliations

  1. Department of Mathematics, Seoul National University, Shinlim-Dong Kwanak-Gu, Seoul, Korea

    Youngmee Kwon

Authors
  1. Youngmee Kwon
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Additional information

Supported by the Global Analysis Research Center at the Seoul National University during the preparation of this manuscript

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Cite this article

Kwon, Y. The submartingal problem for Brownian motion in a cone with non-constant oblique reflection. Probab. Th. Rel. Fields 92, 351–391 (1992). https://doi.org/10.1007/BF01300561

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  • Received: 25 October 1989

  • Revised: 21 November 1991

  • Issue Date: September 1992

  • DOI: https://doi.org/10.1007/BF01300561

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Mathematics Subject Classification (1980)

  • 60G17
  • 60J60
  • 60J65
  • 35J05
  • 35R05
  • 58G32
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