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Distribution of linear fractal interpolation function for random dataset with stable noise. (English) Zbl 1493.60039

Summary: In this paper, we derive the probability distribution of linear fractal interpolation function (FIF) for a random dataset on \(\mathbb{R}^2\), where randomness in the data is induced, using \(\alpha\)-stable noise, in the second coordinate. In particular, we show that the distribution of linear FIF, at any point (on the first coordinate), is also stable, but with different parameters which can be estimated. Finally, we also provide statistical validity of our results.

MSC:

60E07 Infinitely divisible distributions; stable distributions
28A80 Fractals
41A05 Interpolation in approximation theory
41A30 Approximation by other special function classes
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