A class of micropulses and antipersistent fractional Brownian motion
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Abstract
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.Fractal sums of pulses Fractal sums of micropulses Fractional Brownian motion Poisson random measure Self-similarity Self-affinity Stationarity of increments