June 13, 2024Fractal and FractionalOpen Access

Fractional Operators and Fractionally Integrated Random Fields on Zν

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Discussion

Analysis identifies conditions for kernels in fractional operators and random fields with implications for random walks.

The analysis reveals necessary conditions for the invertibility and summability of kernels in fractional integral operators.
Asymptotic behavior of kernels is established under the local limit theorem for random walks.
Observation noted in fractionally integrated random fields suggests a relationship with white noise and scaling limits in Zν space.

Pilipauskaitė et al. (2024) studied this question.

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