A class of micropulses and antipersistent fractional Brownian motion
We begin with stochastic processes obtained as sums of "up-and-down" pulses with random moments of birth [tau] and random lifetime w determined by a Poisson random measure. When the pulse amplitude [var epsilon] --> 0, while the pulse density [delta] increases to infinity, one obtains a process of "fractal sum of micropulses." A CLT style argument shows convergence in the sense of finite dimensional distributions to a Gaussian process with negatively correlated increments. In the most interesting case the limit is fractional Brownian motion (FBM), a self-affine process with the scaling constant . The construction is extended to the multidimensional FBM field as well as to micropulses of more complicated shape.
Year of publication: |
1995
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Authors: | Cioczek-Georges, R. ; Mandelbrot, B. B. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 60.1995, 1, p. 1-18
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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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