Alternative micropulses and fractional Brownian motion
We showed in an earlier paper (1995a) that negatively correlated fractional Brownian motion (FBM) can be generated as a fractal sum of one kind of micropulses (FSM). That is, FBM of exponent is the limit (in the sense of finite-dimensional distributions) of a certain sequence of processes obtained as sums of rectangular pulses. We now show that more general pulses yield a wide range of FBMs: either negatively (as before) or positively () correlated. We begin with triangular (conical and semi-conical) pulses. To transform them into micropulses, the base angle is made to decrease to zero, while the number of pulses, determined by a Poisson random measure, is made to increase to infinity. Then we extend our results to more general pulse shapes.
Year of publication: |
1996
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Authors: | Cioczek-Georges, R. ; Mandelbrot, B. B. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 64.1996, 2, p. 143-152
|
Publisher: |
Elsevier |
Keywords: | Fractal sums of pulses Fractal sums of micropulses Fractional Brownian motion Poisson random measure Self-similarity Self-affinity Stationarity of increments |
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