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1 results

  • The structure of Gaussian fields near a level crossing

  • Richard J. Wilson, Robert J. Adler
  • Journal:
    Advances in Applied Probability / Volume 14 / Issue 3 / September 1982
    Published online by Cambridge University Press:
    01 July 2016, pp. 543-565
    Print publication:
    September 1982

  • In this paper, we investigate the behaviour of a Gaussian random field after an ‘upcrossing' of a particular level. In Section 1, we briefly discuss model processes and their background, and give a definition of an upcrossing of a level for random fields. A model field is constructed for the random field after an upcrossing of a level by using horizontal window conditioning in Section 2. The final section contains asymptotic distributions for the model field and for the location and height of the ‘closest' maximum to the upcrossing as the level becomes arbitrarily high.