Summary
In view of approximating the fractional Brownian process in the plane B. Mandelbrot examined the superimposition of rectilinear faults, centered on the axis of a Poisson process with arbitrary large rate, the profiles of which being of the type Q · sgn(x)¦x¦α, ¦α¦<l/2 and Q a real valued random variable. In the following, we derive from general hypotheses a formula which caracterises any random profile leading to a Gaussian process of given type and thus providing explicit examples of profiles, thinkably less contrived than the former; some results on the quality of convergence are given.
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Fellous, A., Granara, J. Superposition de déformations cylindriques d'axes poissonniens dans le plan. Z. Wahrscheinlichkeitstheorie verw Gebiete 69, 47–64 (1985). https://doi.org/10.1007/BF00532585
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DOI: https://doi.org/10.1007/BF00532585