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Local times of fractional Brownian sheets
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  • Published: October 2002

Local times of fractional Brownian sheets

  • Yimin Xiao1 &
  • Tusheng Zhang2 

Probability Theory and Related Fields volume 124, pages 204–226 (2002)Cite this article

  • 185 Accesses

  • 45 Citations

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Abstract.

 Let be a real-valued fractional Brownian sheet. Consider the (N, d) Gaussian random field B H defined by

where are independent copies of B 0 H. In this paper, the existence and joint continuity of the local times of B H are established.

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Authors and Affiliations

  1. Department of Statistics and Probability, A-413 Wells Hall, Michigan State University, East Lansing, MI 48824, USA. e-mail: xiao@stt.msu.edu, , , , , , US

    Yimin Xiao

  2. Department of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK. e-mail: tzhang@ma.man.ac.uk, , , , , , GB

    Tusheng Zhang

Authors
  1. Yimin Xiao
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  2. Tusheng Zhang
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Additional information

Received: 2 October 2001 / Revised version: 7 January 2002 / Published online: 22 August 2002

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Xiao, Y., Zhang, T. Local times of fractional Brownian sheets. Probab Theory Relat Fields 124, 204–226 (2002). https://doi.org/10.1007/s004400200210

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  • Issue Date: October 2002

  • DOI: https://doi.org/10.1007/s004400200210

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Keywords

  • Local Time
  • Random Field
  • Independent Copy
  • Gaussian Random Field
  • Brownian Sheet
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