Probability Theory and Related Fields

, Volume 73, Issue 1, pp 153–158 | Cite as

A note on certain integral equations associated with non-linear time series analysis

  • K. S. Chan
  • H. Tong
Article

Summary

We consider the integral equation inh\(h(y) = \int\limits_{\mathbb{R}^n } {f(y - \hat Tx)h(x)dx,} \) wheref is a p.d.f. and\(\hat T:\mathbb{R}^n \to \mathbb{R}^n \). It is well known that explicit solutions rarely exist. However, it is shown in this paper that, if certain symmetry exists, the above equation sometimes admits an explicit solution. Illustrations are included.

Keywords

Time Series Integral Equation Stochastic Process Probability Theory Mathematical Biology 

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References

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    Tong, H.: Threshold models in non-linear time series analysis. Lecture Notes in Statistics21. Berlin, Heidelberg, New York, Tokyo: Springer 1983Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • K. S. Chan
    • 1
  • H. Tong
    • 2
  1. 1.City Polytechnic of Hong KongHong Kong
  2. 2.Mathematical InstituteUniversity of Kent at CanterburyCanterburyU.K.

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