Tangent fields and the local structure of random fields

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Abstract

A tangent field of a random field X on R-N at a point z is defined to be the limit of a sequence of scaled enlargements of X about z. This paper develops general properties of tangent fields, emphasising their rich structure and strong invariance properties which place considerable constraints on their form. The theory is illustrated by a variety of examples, both of a smooth and fractal nature.

Original languageEnglish
Pages (from-to)731-750
Number of pages20
JournalJournal of Theoretical Probability
Volume15
Issue number3
DOIs
Publication statusPublished - Jul 2002

Keywords

  • tangent fields
  • random fields
  • fractional brownian fields
  • self-similar processes
  • strong invariance

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