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Alternative micropulses and fractional Brownian motion. (English) Zbl 0879.60076
The generation of fractional Brownian motion (FBM) as a fractal sum of micropulses is considered [cf. B. B. Mandelbrot and J. W. Van Ness, SIAM Rev. 10, 422-437 (1968; Zbl 0179.47801)]). In an earlier paper of the authors [Stochastic Process Appl. 60, 1-8 (1995; Zbl 0846.60055)], rectangular pulses leading to negatively correlated (the self-affinity exponent \(H<1/2\)) FMB’s have been examined. More general pulse shapes are treated here starting with conical and semiconical pulses and ending with Lévy staircase, Cantor pyramid and multifractal staircase. The location of the pulse, its width and height are random, the transformation of a pulse proceeds by letting the tangent of the base angle go to zero. It is shown that only pulses without jumps at their starting and ending points generate positively correlated and ordinary Brown motion (\(H\geq 1/2\)).
Reviewer: Ivan Saxl (Praha)

60J65 Brownian motion
60G18 Self-similar stochastic processes
28A80 Fractals
Full Text: DOI
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