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A note on certain integral equations associated with non-linear time series analysis
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  • Published: March 1986

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

  • K. S. Chan1 &
  • H. Tong2 

Probability Theory and Related Fields volume 73, pages 153–158 (1986)Cite this article

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  • 16 Citations

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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.

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References

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  3. Petrucelli, J.D., Woolford, S.W.: A thresholdAR(1) model. J. Appl. Prob.21, 270–286 (1984)

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Author information

Authors and Affiliations

  1. City Polytechnic of Hong Kong, Hong Kong

    K. S. Chan

  2. Mathematical Institute, University of Kent at Canterbury, CT2 7NF, Canterbury, U.K.

    H. Tong

Authors
  1. K. S. Chan
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  2. H. Tong
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Cite this article

Chan, K.S., Tong, H. A note on certain integral equations associated with non-linear time series analysis. Probab. Th. Rel. Fields 73, 153–158 (1986). https://doi.org/10.1007/BF01845999

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  • Received: 19 November 1985

  • Issue Date: March 1986

  • DOI: https://doi.org/10.1007/BF01845999

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Keywords

  • Time Series
  • Integral Equation
  • Stochastic Process
  • Probability Theory
  • Mathematical Biology
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