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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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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DOI: https://doi.org/10.1007/BF01845999
Keywords
- Time Series
- Integral Equation
- Stochastic Process
- Probability Theory
- Mathematical Biology