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Subordinated Random Fields: Construction of Self-similar Fields

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Part of the Lecture Notes in Mathematics book series (LNM,volume 849)

Abstract

We give a complete characterization of the so-called subordinated random fields of a stationary Gaussian random field. This result enables us to construct new, non-trivial (subordinated) self-similar random fields, i.e. such random fields which may appear as the limit random field in limit theorems. To tell whether the formulas defining these subordinated random fields are meaningful or not we have to decide whether certain classical integrals are convergent or divergent. Hence this chapter contains some results in this direction.

Keywords

  • Self-similar Random Fields
  • Stationary Gaussian Random Field
  • Generalized Field Case
  • Random Spectral Measure
  • Renormalization Group Transformation

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References

  1. Gelfand, I.M., Vilenkin, N.Ya.: Generalized Functions. IV. Some Applications of Harmonic Analysis. Academic (Harcourt, Brace Jovanovich Publishers), New York (1964)

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© 2014 Springer International Publishing Switzerland

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Major, P. (2014). Subordinated Random Fields: Construction of Self-similar Fields. In: Multiple Wiener-Itô Integrals. Lecture Notes in Mathematics, vol 849. Springer, Cham. https://doi.org/10.1007/978-3-319-02642-8_6

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