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A class of micropulses and antipersistent fractional Brownian motion

R. Cioczek-Georges and Benoît Mandelbrot

Stochastic Processes and their Applications, 1995, vol. 60, issue 1, 1-18

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.

Keywords: Fractal; sums; of; pulses; Fractal; sums; of; micropulses; Fractional; Brownian; motion; Poisson; random; measure; Self-similarity; Self-affinity; Stationarity; of; increments (search for similar items in EconPapers)
Date: 1995
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